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Asymptotic results for sums and extremes J. Appl. Probab. (IF 1.0) Pub Date : 2024-03-13 Rita Giuliano, Claudio Macci, Barbara Pacchiarotti
The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability of some random variables to a constant, and a weak convergence to a centered Gaussian distribution (when such random variables are properly centered and rescaled). We talk about noncentral moderate deviations when the weak
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Color-avoiding percolation and branching processes J. Appl. Probab. (IF 1.0) Pub Date : 2024-03-08 Panna Tímea Fekete, Roland Molontay, Balázs Ráth, Kitti Varga
We study a variant of the color-avoiding percolation model introduced by Krause et al., namely we investigate the color-avoiding bond percolation setup on (not necessarily properly) edge-colored Erdős–Rényi random graphs. We say that two vertices are color-avoiding connected in an edge-colored graph if, after the removal of the edges of any color, they are in the same component in the remaining graph
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Skew Ornstein–Uhlenbeck processes with sticky reflection and their applications to bond pricing J. Appl. Probab. (IF 1.0) Pub Date : 2024-03-06 Shiyu Song, Guangli Xu
We study a skew Ornstein–Uhlenbeck process with zero being a sticky reflecting boundary, which is defined as the weak solution to a stochastic differential equation (SDE) system involving local time. The main results obtained include: (i) the existence and uniqueness of solutions to the SDE system, (ii) the scale function and speed measure, and (iii) the distributional properties regarding the transition
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Analysis of -ary tree algorithms with successive interference cancellation J. Appl. Probab. (IF 1.0) Pub Date : 2024-02-26 Quirin Vogel, Yash Deshpande, Cedomir Stefanović, Wolfgang Kellerer
We calculate the mean throughput, number of collisions, successes, and idle slots for random tree algorithms with successive interference cancellation. Except for the case of the throughput for the binary tree, all the results are new. We furthermore disprove the claim that only the binary tree maximizes throughput. Our method works with many observables and can be used as a blueprint for further analysis
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Average Jaccard index of random graphs J. Appl. Probab. (IF 1.0) Pub Date : 2024-02-26 Qunqiang Feng, Shuai Guo, Zhishui Hu
The asymptotic behavior of the Jaccard index in G(n, p), the classical Erdös–Rényi random graph model, is studied as n goes to infinity. We first derive the asymptotic distribution of the Jaccard index of any pair of distinct vertices, as well as the first two moments of this index. Then the average of the Jaccard indices over all vertex pairs in G(n, p) is shown to be asymptotically normal under an
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Connectivity of random graphs after centrality-based vertex removal J. Appl. Probab. (IF 1.0) Pub Date : 2024-02-23 Remco van der Hofstad, Manish Pandey
Centrality measures aim to indicate who is important in a network. Various notions of ‘being important’ give rise to different centrality measures. In this paper, we study how important the central vertices are for the connectivity structure of the network, by investigating how the removal of the most central vertices affects the number of connected components and the size of the giant component. We
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Continuous dependence of stationary distributions on parameters for stochastic predator–prey models J. Appl. Probab. (IF 1.0) Pub Date : 2024-02-22 Nguyen Duc Toan, Nguyen Thanh Dieu, Nguyen Huu Du, Le Ba Dung
This research studies the robustness of permanence and the continuous dependence of the stationary distribution on the parameters for a stochastic predator–prey model with Beddington–DeAngelis functional response. We show that if the model is extinct (resp. permanent) for a parameter, it is still extinct (resp. permanent) in a neighbourhood of this parameter. In the case of extinction, the Lyapunov
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An exponential nonuniform Berry–Esseen bound of the maximum likelihood estimator in a Jacobi process J. Appl. Probab. (IF 1.0) Pub Date : 2024-02-14 Hui Jiang, Qihao Lin, Shaochen Wang
We establish the exponential nonuniform Berry–Esseen bound for the maximum likelihood estimator of unknown drift parameter in an ultraspherical Jacobi process using the change of measure method and precise asymptotic analysis techniques. As applications, the optimal uniform Berry–Esseen bound and optimal Cramér-type moderate deviation for the corresponding maximum likelihood estimator are obtained
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Inference on the intraday spot volatility from high-frequency order prices with irregular microstructure noise J. Appl. Probab. (IF 1.0) Pub Date : 2024-02-14 Markus Bibinger
We consider estimation of the spot volatility in a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices. Based on discrete, noisy observations of an Itô semimartingale with jumps and general stochastic volatility, we present a simple and explicit estimator using local order statistics. We establish consistency and stable central limit theorems as asymptotic
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On some semi-parametric estimates for European option prices J. Appl. Probab. (IF 1.0) Pub Date : 2024-02-14 Carlo Marinelli
We show that an estimate by de la Peña, Ibragimov, and Jordan for ${\mathbb{E}}(X-c)^+$ , with c a constant and X a random variable of which the mean, the variance, and $\mathbb{P}(X \leqslant c)$ are known, implies an estimate by Scarf on the infimum of ${\mathbb{E}}(X \wedge c)$ over the set of positive random variables X with fixed mean and variance. This also shows, as a consequence, that the former
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Scaling limit of the local time of random walks conditioned to stay positive J. Appl. Probab. (IF 1.0) Pub Date : 2024-02-13 Wenming Hong, Mingyang Sun
We prove that the local time of random walks conditioned to stay positive converges to the corresponding local time of three-dimensional Bessel processes by proper scaling. Our proof is based on Tanaka’s pathwise construction for conditioned random walks and the derivation of asymptotics for mixed moments of the local time.
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De Finetti’s control problem with a concave bound on the control rate J. Appl. Probab. (IF 1.0) Pub Date : 2024-01-25 Félix Locas, Jean-François Renaud
We consider De Finetti’s control problem for absolutely continuous strategies with control rates bounded by a concave function and prove that a generalized mean-reverting strategy is optimal in a Brownian model. In order to solve this problem, we need to deal with a nonlinear Ornstein–Uhlenbeck process. Despite the level of generality of the bound imposed on the rate, an explicit expression for the
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Approximation with ergodic processes and testability J. Appl. Probab. (IF 1.0) Pub Date : 2024-01-23 Isaac Loh
We show that stationary time series can be uniformly approximated over all finite time intervals by mixing, non-ergodic, non-mean-ergodic, and periodic processes, and by codings of aperiodic processes. A corollary is that the ergodic hypothesis—that time averages will converge to their statistical counterparts—and several adjacent hypotheses are not testable in the non-parametric case. Further Baire
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SIR model with social gatherings J. Appl. Probab. (IF 1.0) Pub Date : 2024-01-15 Roberto Cortez
We introduce an extension to Kermack and McKendrick’s classic susceptible–infected–recovered (SIR) model in epidemiology, whose underlying mechanism of infection consists of individuals attending randomly generated social gatherings. This gives rise to a system of ordinary differential equations (ODEs) where the force of the infection term depends non-linearly on the proportion of infected individuals
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Sharp large deviations and concentration inequalities for the number of descents in a random permutation J. Appl. Probab. (IF 1.0) Pub Date : 2024-01-05 Bernard Bercu, Michel Bonnefont, Adrien Richou
The goal of this paper is to go further in the analysis of the behavior of the number of descents in a random permutation. Via two different approaches relying on a suitable martingale decomposition or on the Irwin–Hall distribution, we prove that the number of descents satisfies a sharp large-deviation principle. A very precise concentration inequality involving the rate function in the large-deviation
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On the Kolmogorov constant explicit form in the theory of discrete-time stochastic branching systems J. Appl. Probab. (IF 1.0) Pub Date : 2024-01-04 Azam A. Imomov, Misliddin S. Murtazaev
We consider a discrete-time population growth system called the Bienaymé–Galton–Watson stochastic branching system. We deal with a noncritical case, in which the per capita offspring mean $m\neq1$ . The famous Kolmogorov theorem asserts that the expectation of the population size in the subcritical case $m<1$ on positive trajectories of the system asymptotically stabilizes and approaches ${1}/\mathcal{K}$
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Weak convergence of the extremes of branching Lévy processes with regularly varying tails J. Appl. Probab. (IF 1.0) Pub Date : 2023-12-06 Yan-xia Ren, Renming Song, Rui Zhang
We study the weak convergence of the extremes of supercritical branching Lévy processes $\{\mathbb{X}_t, t \ge0\}$ whose spatial motions are Lévy processes with regularly varying tails. The result is drastically different from the case of branching Brownian motions. We prove that, when properly renormalized, $\mathbb{X}_t$ converges weakly. As a consequence, we obtain a limit theorem for the order
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Speed of extinction for continuous-state branching processes in a weakly subcritical Lévy environment J. Appl. Probab. (IF 1.0) Pub Date : 2023-12-01 Natalia Cardona-Tobón, Juan Carlos Pardo
We continue with the systematic study of the speed of extinction of continuous-state branching processes in Lévy environments under more general branching mechanisms. Here, we deal with the weakly subcritical regime under the assumption that the branching mechanism is regularly varying. We extend recent results of Li and Xu (2018) and Palau et al. (2016), where it is assumed that the branching mechanism
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Dynamics of information networks J. Appl. Probab. (IF 1.0) Pub Date : 2023-11-30 Andrei Sontag, Tim Rogers, Christian A Yates
We explore a simple model of network dynamics which has previously been applied to the study of information flow in the context of epidemic spreading. A random rooted network is constructed that evolves according to the following rule: at a constant rate, pairs of nodes (i, j) are randomly chosen to interact, with an edge drawn from i to j (and any other out-edge from i deleted) if j is strictly closer
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Local convergence of critical Galton–Watson trees J. Appl. Probab. (IF 1.0) Pub Date : 2023-11-30 Aymen Bouaziz
We study the local convergence of critical Galton–Watson trees under various conditionings. We give a sufficient condition, which serves to cover all previous known results, for the convergence in distribution of a conditioned Galton–Watson tree to Kesten’s tree. We also propose a new proof to give the limit in distribution of a critical Galton–Watson tree, with finite support, conditioned on having
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Characteristics of the switch process and geometric divisibility J. Appl. Probab. (IF 1.0) Pub Date : 2023-11-06 Henrik Bengtsson
The switch process alternates independently between 1 and $-1$ , with the first switch to 1 occurring at the origin. The expected value function of this process is defined uniquely by the distribution of switching times. The relation between the two is implicitly described through the Laplace transform, which is difficult to use for determining if a given function is the expected value function of
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Tessellation-valued processes that are generated by cell division J. Appl. Probab. (IF 1.0) Pub Date : 2023-11-01 Servet Martínez, Werner Nagel
Processes of random tessellations of the Euclidean space $\mathbb{R}^d$ , $d\geq 1$ , are considered that are generated by subsequent division of their cells. Such processes are characterized by the laws of the life times of the cells until their division and by the laws for the random hyperplanes that divide the cells at the end of their life times. The STIT (STable with respect to ITerations) tessellation
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A large-deviation principle for birth–death processes with a linear rate of downward jumps J. Appl. Probab. (IF 1.0) Pub Date : 2023-10-31 Artem Logachov, Yuri Suhov, Nikita Vvedenskaya, Anatoly Yambartsev
Birth–death processes form a natural class where ideas and results on large deviations can be tested. We derive a large-deviation principle under an assumption that the rate of jump down (death) grows asymptotically linearly with the population size, while the rate of jump up (birth) grows sublinearly. We establish a large-deviation principle under various forms of scaling of the underlying process
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Trajectory fitting estimation for reflected stochastic linear differential equations of a large signal J. Appl. Probab. (IF 1.0) Pub Date : 2023-10-31 Xuekang Zhang, Huisheng Shu
In this paper we study the drift parameter estimation for reflected stochastic linear differential equations of a large signal. We discuss the consistency and asymptotic distributions of trajectory fitting estimator (TFE).
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On a time-changed variant of the generalized counting process J. Appl. Probab. (IF 1.0) Pub Date : 2023-10-27 M. Khandakar, K. K. Kataria
In this paper, we time-change the generalized counting process (GCP) by an independent inverse mixed stable subordinator to obtain a fractional version of the GCP. We call it the mixed fractional counting process (MFCP). The system of fractional differential equations that governs its state probabilities is obtained using the Z transform method. Its one-dimensional distribution, mean, variance, covariance
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Boolean percolation on digraphs and random exchange processes J. Appl. Probab. (IF 1.0) Pub Date : 2023-10-25 Georg Braun
We study in a general graph-theoretic formulation a long-range percolation model introduced by Lamperti [27]. For various underlying digraphs, we discuss connections between this model and random exchange processes. We clarify, for all $n \in \mathbb{N}$ , under which conditions the lattices $\mathbb{N}_0^n$ and $\mathbb{Z}^n$ are essentially covered in this model. Moreover, for all $n \geq 2$ , we
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The unified extropy and its versions in classical and Dempster–Shafer theories J. Appl. Probab. (IF 1.0) Pub Date : 2023-10-23 Francesco Buono, Yong Deng, Maria Longobardi
Measures of uncertainty are a topic of considerable and growing interest. Recently, the introduction of extropy as a measure of uncertainty, dual to Shannon entropy, has opened up interest in new aspects of the subject. Since there are many versions of entropy, a unified formulation has been introduced to work with all of them in an easy way. Here we consider the possibility of defining a unified formulation
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Aging notions, stochastic orders, and expected utilities J. Appl. Probab. (IF 1.0) Pub Date : 2023-10-18 Jianping Yang, Weiwei Zhuang, Taizhong Hu
There are some connections between aging notions, stochastic orders, and expected utilities. It is known that the DRHR (decreasing reversed hazard rate) aging notion can be characterized via the comparative statics result of risk aversion, and that the location-independent riskier order preserves monotonicity between risk premium and the Arrow–Pratt measure of risk aversion, and that the dispersive
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Central limit theorem in complete feedback games J. Appl. Probab. (IF 1.0) Pub Date : 2023-10-16 Andrea Ottolini, Raghavendra Tripathi
Consider a well-shuffled deck of cards of n different types where each type occurs m times. In a complete feedback game, a player is asked to guess the top card from the deck. After each guess, the top card is revealed to the player and is removed from the deck. The total number of correct guesses in a complete feedback game has attracted significant interest in the past few decades. Under different
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Resolving an old problem on the preservation of the IFR property under the formation of -out-of- systems with discrete distributions J. Appl. Probab. (IF 1.0) Pub Date : 2023-10-16 Mahdi Alimohammadi, Jorge Navarro
More than half a century ago, it was proved that the increasing failure rate (IFR) property is preserved under the formation of k-out-of-n systems (order statistics) when the lifetimes of the components are independent and have a common absolutely continuous distribution function. However, this property has not yet been proved in the discrete case. Here we give a proof based on the log-concavity property
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Stochastic ordering results on the duration of the gambler’s ruin game J. Appl. Probab. (IF 1.0) Pub Date : 2023-10-06 Shoou-Ren Hsiau, Yi-Ching Yao
In the classical gambler’s ruin problem, the gambler plays an adversary with initial capitals z and $a-z$ , respectively, where $a>0$ and $0< z < a$ are integers. At each round, the gambler wins or loses a dollar with probabilities p and $1-p$ . The game continues until one of the two players is ruined. For even a and $0
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Optimal stopping methodology for the secretary problem with random queries J. Appl. Probab. (IF 1.0) Pub Date : 2023-10-02 George V. Moustakides, Xujun Liu, Olgica Milenkovic
Candidates arrive sequentially for an interview process which results in them being ranked relative to their predecessors. Based on the ranks available at each time, a decision mechanism must be developed that selects or dismisses the current candidate in an effort to maximize the chance of selecting the best. This classical version of the ‘secretary problem’ has been studied in depth, mostly using
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Stochastic differential equation approximations of generative adversarial network training and its long-run behavior J. Appl. Probab. (IF 1.0) Pub Date : 2023-10-02 Haoyang Cao, Xin Guo
This paper analyzes the training process of generative adversarial networks (GANs) via stochastic differential equations (SDEs). It first establishes SDE approximations for the training of GANs under stochastic gradient algorithms, with precise error bound analysis. It then describes the long-run behavior of GAN training via the invariant measures of its SDE approximations under proper conditions.
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R-positivity and the existence of zero-temperature limits of Gibbs measures on nearest-neighbor matrices J. Appl. Probab. (IF 1.0) Pub Date : 2023-09-25 Jorge Littin Curinao, Gerardo Corredor Rincón
We study the $R_\beta$ -positivity and the existence of zero-temperature limits for a sequence of infinite-volume Gibbs measures $(\mu_{\beta}(\!\cdot\!))_{\beta \geq 0}$ at inverse temperature $\beta$ associated to a family of nearest-neighbor matrices $(Q_{\beta})_{\beta \geq 0}$ reflected at the origin. We use a probabilistic approach based on the continued fraction theory previously introduced
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Comparison theorem and stability under perturbation of transition rate matrices for regime-switching processes J. Appl. Probab. (IF 1.0) Pub Date : 2023-09-14 Jinghai Shao
A comparison theorem for state-dependent regime-switching diffusion processes is established, which enables us to pathwise-control the evolution of the state-dependent switching component simply by Markov chains. Moreover, a sharp estimate on the stability of Markovian regime-switching processes under the perturbation of transition rate matrices is provided. Our approach is based on elaborate constructions
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Strong convergence of peaks over a threshold J. Appl. Probab. (IF 1.0) Pub Date : 2023-08-23 Simone A. Padoan, Stefano Rizzelli
Extreme value theory plays an important role in providing approximation results for the extremes of a sequence of independent random variables when their distribution is unknown. An important one is given by the generalised Pareto distribution $H_\gamma(x)$ as an approximation of the distribution $F_t(s(t)x)$ of the excesses over a threshold t, where s(t) is a suitable norming function. We study the
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Normal and stable approximation to subgraph counts in superpositions of Bernoulli random graphs J. Appl. Probab. (IF 1.0) Pub Date : 2023-08-18 Mindaugas Bloznelis, Joona Karjalainen, Lasse Leskelä
Real networks often exhibit clustering, the tendency to form relatively small groups of nodes with high edge densities. This clustering property can cause large numbers of small and dense subgraphs to emerge in otherwise sparse networks. Subgraph counts are an important and commonly used source of information about the network structure and function. We study probability distributions of subgraph counts
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Reliability analyses of linear two-dimensional consecutive k-type systems J. Appl. Probab. (IF 1.0) Pub Date : 2023-08-14 He Yi, Narayanaswamy Balakrishnan, Xiang Li
In this paper, several linear two-dimensional consecutive k-type systems are studied, which include the linear connected-(k, r)-out-of- $(m,n)\colon\! F$ system and the linear l-connected-(k, r)-out-of- $(m,n)\colon\! F$ system without/with overlapping. Reliabilities of these systems are studied via the finite Markov chain imbedding approach (FMCIA) in a novel way. Some numerical examples are provided
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Stopping problems with an unknown state J. Appl. Probab. (IF 1.0) Pub Date : 2023-08-09 Erik Ekström, Yuqiong Wang
We extend the classical setting of an optimal stopping problem under full information to include problems with an unknown state. The framework allows the unknown state to influence (i) the drift of the underlying process, (ii) the payoff functions, and (iii) the distribution of the time horizon. Since the stopper is assumed to observe the underlying process and the random horizon, this is a two-source
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Chase–escape in dynamic device-to-device networks J. Appl. Probab. (IF 1.0) Pub Date : 2023-08-07 Elie Cali, Alexander Hinsen, Benedikt Jahnel, Jean-Philippe Wary
We feature results on global survival and extinction of an infection in a multi-layer network of mobile agents. Expanding on a model first presented in Cali et al. (2022), we consider an urban environment, represented by line segments in the plane, in which agents move according to a random waypoint model based on a Poisson point process. Whenever two agents are at sufficiently close proximity for
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Heavy-traffic limits for parallel single-server queues with randomly split Hawkes arrival processes J. Appl. Probab. (IF 1.0) Pub Date : 2023-08-07 Bo Li, Guodong Pang
We consider parallel single-server queues in heavy traffic with randomly split Hawkes arrival processes. The service times are assumed to be independent and identically distributed (i.i.d.) in each queue and are independent in different queues. In the critically loaded regime at each queue, it is shown that the diffusion-scaled queueing and workload processes converge to a multidimensional reflected
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The proportion of triangles in a class of anisotropic Poisson line tessellations J. Appl. Probab. (IF 1.0) Pub Date : 2023-08-07 Nils Heerten, Julia Krecklenberg, Christoph Thäle
Stationary Poisson processes of lines in the plane are studied, whose directional distributions are concentrated on $k\geq 3$ equally spread directions. The random lines of such processes decompose the plane into a collection of random polygons, which form a so-called Poisson line tessellation. The focus of this paper is to determine the proportion of triangles in such tessellations, or equivalently
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Duality theory for exponential utility-based hedging in the Almgren–Chriss model J. Appl. Probab. (IF 1.0) Pub Date : 2023-08-03 Yan Dolinsky
In this paper we obtain a duality result for the exponential utility maximization problem where trading is subject to quadratic transaction costs and the investor is required to liquidate her position at the maturity date. As an application of the duality, we treat utility-based hedging in the Bachelier model. For European contingent claims with a quadratic payoff, we compute the optimal trading strategy
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On the joint survival probability of two collaborating firms J. Appl. Probab. (IF 1.0) Pub Date : 2023-08-01 Stefan Ankirchner, Robert Hesse, Maike Klein
We consider the problem of controlling the drift and diffusion rate of the endowment processes of two firms such that the joint survival probability is maximized. We assume that the endowment processes are continuous diffusions, driven by independent Brownian motions, and that the aggregate endowment is a Brownian motion with constant drift and diffusion rate. Our results reveal that the maximal joint
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Phase transition for the generalized two-community stochastic block model J. Appl. Probab. (IF 1.0) Pub Date : 2023-07-31 Sunmin Lee, Ji Oon Lee
We study the problem of detecting the community structure from the generalized stochastic block model with two communities (G2-SBM). Based on analysis of the Stieljtes transform of the empirical spectral distribution, we prove a Baik–Ben Arous–Péché (BBP)-type transition for the largest eigenvalue of the G2-SBM. For specific models, such as a hidden community model and an unbalanced stochastic block
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Characterization of the optimal average cost in Markov decision chains driven by a risk-seeking controller J. Appl. Probab. (IF 1.0) Pub Date : 2023-07-21 Rolando Cavazos-Cadena, Hugo Cruz-Suárez, Raúl Montes-de-Oca
This work concerns Markov decision chains on a denumerable state space endowed with a bounded cost function. The performance of a control policy is assessed by a long-run average criterion as measured by a risk-seeking decision maker with constant risk-sensitivity. Besides standard continuity–compactness conditions, the framework of the paper is determined by the following conditions: (i) the state
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An elementary approach to the inverse first-passage-time problem for soft-killed Brownian motion J. Appl. Probab. (IF 1.0) Pub Date : 2023-07-04 Alexander Klump, Martin Kolb
We prove existence and uniqueness for the inverse-first-passage time problem for soft-killed Brownian motion using rather elementary methods relying on basic results from probability theory only. We completely avoid the relation to a suitable partial differential equation via a suitable Feynman–Kac representation, which was previously one of the main tools.
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Optimal coupling of jumpy Brownian motion on the circle J. Appl. Probab. (IF 1.0) Pub Date : 2023-07-04 Stephen B. Connor, Roberta Merli
Consider a Brownian motion on the circumference of the unit circle, which jumps to the opposite point of the circumference at incident times of an independent Poisson process of rate $\lambda$. We examine the problem of coupling two copies of this ‘jumpy Brownian motion’ started from different locations, so as to optimise certain functions of the coupling time. We describe two intuitive co-adapted
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Weakly interacting oscillators on dense random graphs J. Appl. Probab. (IF 1.0) Pub Date : 2023-06-30 Gianmarco Bet, Fabio Coppini, Francesca Romana Nardi
We consider a class of weakly interacting particle systems of mean-field type. The interactions between the particles are encoded in a graph sequence, i.e. two particles are interacting if and only if they are connected in the underlying graph. We establish a law of large numbers for the empirical measure of the system that holds whenever the graph sequence is convergent to a graphon. The limit is
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Differences between Lyapunov exponents for the simple random walk in Bernoulli potentials J. Appl. Probab. (IF 1.0) Pub Date : 2023-06-23 Naoki Kubota
We consider the simple random walk on the d-dimensional lattice $\mathbb{Z}^d$ ($d \geq 1$), traveling in potentials which are Bernoulli-distributed. The so-called Lyapunov exponent describes the cost of traveling for the simple random walk in the potential, and it is known that the Lyapunov exponent is strictly monotone in the parameter of the Bernoulli distribution. Hence the aim of this paper is
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Information-theoretic convergence of extreme values to the Gumbel distribution J. Appl. Probab. (IF 1.0) Pub Date : 2023-06-21 Oliver Johnson
We show how convergence to the Gumbel distribution in an extreme value setting can be understood in an information-theoretic sense. We introduce a new type of score function which behaves well under the maximum operation, and which implies simple expressions for entropy and relative entropy. We show that, assuming certain properties of the von Mises representation, convergence to the Gumbel distribution
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Monotonicity of implied volatility for perpetual put options J. Appl. Probab. (IF 1.0) Pub Date : 2023-06-19 Erik Ekström, Ebba Mellquist
We define and study properties of implied volatility for American perpetual put options. In particular, we show that if the market prices are derived from a local volatility model with a monotone volatility function, then the corresponding implied volatility is also monotone as a function of the strike price.
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Explosion of continuous-state branching processes with competition in a Lévy environment J. Appl. Probab. (IF 1.0) Pub Date : 2023-06-09 Rugang Ma, Xiaowen Zhou
We find sufficient conditions on explosion/non-explosion for continuous-state branching processes with competition in a Lévy random environment. In particular, we identify the necessary and sufficient conditions on explosion/non-explosion when the competition function is a power function and the Lévy measure of the associated branching mechanism is stable.
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On relevation redundancy to coherent systems at component and system levels J. Appl. Probab. (IF 1.0) Pub Date : 2023-06-09 Chen Li, Xiaohu Li
Recently, the relevation transformation has received further attention from researchers, and some interesting results have been developed. It is well known that the active redundancy at component level results in a more reliable coherent system than that at system level. However, the lack of study of this problem with relevation redundancy prevents us from fully understanding such a generalization
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On a wider class of prior distributions for graphical models J. Appl. Probab. (IF 1.0) Pub Date : 2023-06-08 Abhinav Natarajan, Willem van den Boom, Kristoforus Bryant Odang, Maria de Iorio
Gaussian graphical models are useful tools for conditional independence structure inference of multivariate random variables. Unfortunately, Bayesian inference of latent graph structures is challenging due to exponential growth of $\mathcal{G}_n$, the set of all graphs in n vertices. One approach that has been proposed to tackle this problem is to limit search to subsets of $\mathcal{G}_n$. In this
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Extrema of a multinomial assignment process J. Appl. Probab. (IF 1.0) Pub Date : 2023-06-06 Mikhail Lifshits, Gilles Mordant
We study the asymptotic behaviour of the expectation of the maxima and minima of a random assignment process generated by a large matrix with multinomial entries. A variety of results is obtained for different sparsity regimes.
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Tail variance allocation, Shapley value, and the majorization problem J. Appl. Probab. (IF 1.0) Pub Date : 2023-06-06 Marcello Galeotti, Giovanni Rabitti
With a focus on the risk contribution in a portofolio of dependent risks, Colini-Baldeschi et al. (2018) introduced Shapley values for variance and standard deviation games. In this note we extend their results, introducing tail variance as well as tail standard deviation games. We derive closed-form expressions for the Shapley values for the tail variance game and we analyze the vector majorization
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Exact convergence analysis for metropolis–hastings independence samplers in Wasserstein distances J. Appl. Probab. (IF 1.0) Pub Date : 2023-06-05 Austin Brown, Galin L. Jones
Under mild assumptions, we show that the exact convergence rate in total variation is also exact in weaker Wasserstein distances for the Metropolis–Hastings independence sampler. We develop a new upper and lower bound on the worst-case Wasserstein distance when initialized from points. For an arbitrary point initialization, we show that the convergence rate is the same and matches the convergence rate
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Moderate deviations inequalities for Gaussian process regression J. Appl. Probab. (IF 1.0) Pub Date : 2023-06-05 Jialin Li, Ilya O. Ryzhov
Gaussian process regression is widely used to model an unknown function on a continuous domain by interpolating a discrete set of observed design points. We develop a theoretical framework for proving new moderate deviations inequalities on different types of error probabilities that arise in GP regression. Two specific examples of broad interest are the probability of falsely ordering pairs of points
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Extropy: Characterizations and dynamic versions J. Appl. Probab. (IF 1.0) Pub Date : 2023-06-02 Abdolsaeed Toomaj, Majid Hashempour, Narayanaswamy Balakrishnan
Several information measures have been proposed and studied in the literature. One such measure is extropy, a complementary dual function of entropy. Its meaning and related aging notions have not yet been studied in great detail. In this paper, we first illustrate that extropy information ranks the uniformity of a wide array of absolutely continuous families. We then discuss several theoretical merits