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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 : 20240214
Hui Jiang, Qihao Lin, Shaochen WangWe 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 Cramértype moderate deviation for the corresponding maximum likelihood estimator are obtained

Inference on the intraday spot volatility from highfrequency order prices with irregular microstructure noise J. Appl. Probab. (IF 1.0) Pub Date : 20240214
Markus BibingerWe consider estimation of the spot volatility in a stochastic boundary model with onesided microstructure noise for highfrequency 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

On some semiparametric estimates for European option prices J. Appl. Probab. (IF 1.0) Pub Date : 20240214
Carlo MarinelliWe show that an estimate by de la Peña, Ibragimov, and Jordan for ${\mathbb{E}}(Xc)^+$ , 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

Scaling limit of the local time of random walks conditioned to stay positive J. Appl. Probab. (IF 1.0) Pub Date : 20240213
Wenming Hong, Mingyang SunWe prove that the local time of random walks conditioned to stay positive converges to the corresponding local time of threedimensional 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.

De Finetti’s control problem with a concave bound on the control rate J. Appl. Probab. (IF 1.0) Pub Date : 20240125
Félix Locas, JeanFrançois RenaudWe consider De Finetti’s control problem for absolutely continuous strategies with control rates bounded by a concave function and prove that a generalized meanreverting 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

Approximation with ergodic processes and testability J. Appl. Probab. (IF 1.0) Pub Date : 20240123
Isaac LohWe show that stationary time series can be uniformly approximated over all finite time intervals by mixing, nonergodic, nonmeanergodic, 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 nonparametric case. Further Baire

SIR model with social gatherings J. Appl. Probab. (IF 1.0) Pub Date : 20240115
Roberto CortezWe 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 nonlinearly on the proportion of infected individuals

Sharp large deviations and concentration inequalities for the number of descents in a random permutation J. Appl. Probab. (IF 1.0) Pub Date : 20240105
Bernard Bercu, Michel Bonnefont, Adrien RichouThe 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 largedeviation principle. A very precise concentration inequality involving the rate function in the largedeviation

On the Kolmogorov constant explicit form in the theory of discretetime stochastic branching systems J. Appl. Probab. (IF 1.0) Pub Date : 20240104
Azam A. Imomov, Misliddin S. MurtazaevWe consider a discretetime 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 ${1}/\mathcal{K}$

Weak convergence of the extremes of branching Lévy processes with regularly varying tails J. Appl. Probab. (IF 1.0) Pub Date : 20231206
Yanxia Ren, Renming Song, Rui ZhangWe 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

Speed of extinction for continuousstate branching processes in a weakly subcritical Lévy environment J. Appl. Probab. (IF 1.0) Pub Date : 20231201
Natalia CardonaTobón, Juan Carlos PardoWe continue with the systematic study of the speed of extinction of continuousstate 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

Dynamics of information networks J. Appl. Probab. (IF 1.0) Pub Date : 20231130
Andrei Sontag, Tim Rogers, Christian A YatesWe 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 outedge from i deleted) if j is strictly closer

Local convergence of critical Galton–Watson trees J. Appl. Probab. (IF 1.0) Pub Date : 20231130
Aymen BouazizWe 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

Characteristics of the switch process and geometric divisibility J. Appl. Probab. (IF 1.0) Pub Date : 20231106
Henrik BengtssonThe 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

Tessellationvalued processes that are generated by cell division J. Appl. Probab. (IF 1.0) Pub Date : 20231101
Servet Martínez, Werner NagelProcesses 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

A largedeviation principle for birth–death processes with a linear rate of downward jumps J. Appl. Probab. (IF 1.0) Pub Date : 20231031
Artem Logachov, Yuri Suhov, Nikita Vvedenskaya, Anatoly YambartsevBirth–death processes form a natural class where ideas and results on large deviations can be tested. We derive a largedeviation 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 largedeviation principle under various forms of scaling of the underlying process

Trajectory fitting estimation for reflected stochastic linear differential equations of a large signal J. Appl. Probab. (IF 1.0) Pub Date : 20231031
Xuekang Zhang, Huisheng ShuIn 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).

On a timechanged variant of the generalized counting process J. Appl. Probab. (IF 1.0) Pub Date : 20231027
M. Khandakar, K. K. KatariaIn this paper, we timechange 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 onedimensional distribution, mean, variance, covariance

Boolean percolation on digraphs and random exchange processes J. Appl. Probab. (IF 1.0) Pub Date : 20231025
Georg BraunWe study in a general graphtheoretic formulation a longrange 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

The unified extropy and its versions in classical and Dempster–Shafer theories J. Appl. Probab. (IF 1.0) Pub Date : 20231023
Francesco Buono, Yong Deng, Maria LongobardiMeasures 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

Aging notions, stochastic orders, and expected utilities J. Appl. Probab. (IF 1.0) Pub Date : 20231018
Jianping Yang, Weiwei Zhuang, Taizhong HuThere 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 locationindependent riskier order preserves monotonicity between risk premium and the Arrow–Pratt measure of risk aversion, and that the dispersive

Central limit theorem in complete feedback games J. Appl. Probab. (IF 1.0) Pub Date : 20231016
Andrea Ottolini, Raghavendra TripathiConsider a wellshuffled 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

Resolving an old problem on the preservation of the IFR property under the formation of outof systems with discrete distributions J. Appl. Probab. (IF 1.0) Pub Date : 20231016
Mahdi Alimohammadi, Jorge NavarroMore than half a century ago, it was proved that the increasing failure rate (IFR) property is preserved under the formation of koutofn 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 logconcavity property

Stochastic ordering results on the duration of the gambler’s ruin game J. Appl. Probab. (IF 1.0) Pub Date : 20231006
ShoouRen Hsiau, YiChing YaoIn the classical gambler’s ruin problem, the gambler plays an adversary with initial capitals z and $az$ , respectively, where $a>0$ and $0< z < a$ are integers. At each round, the gambler wins or loses a dollar with probabilities p and $1p$ . The game continues until one of the two players is ruined. For even a and $0

Optimal stopping methodology for the secretary problem with random queries J. Appl. Probab. (IF 1.0) Pub Date : 20231002
George V. Moustakides, Xujun Liu, Olgica MilenkovicCandidates 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

Stochastic differential equation approximations of generative adversarial network training and its longrun behavior J. Appl. Probab. (IF 1.0) Pub Date : 20231002
Haoyang Cao, Xin GuoThis 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 longrun behavior of GAN training via the invariant measures of its SDE approximations under proper conditions.

Rpositivity and the existence of zerotemperature limits of Gibbs measures on nearestneighbor matrices J. Appl. Probab. (IF 1.0) Pub Date : 20230925
Jorge Littin Curinao, Gerardo Corredor RincónWe study the $R_\beta$ positivity and the existence of zerotemperature limits for a sequence of infinitevolume Gibbs measures $(\mu_{\beta}(\!\cdot\!))_{\beta \geq 0}$ at inverse temperature $\beta$ associated to a family of nearestneighbor matrices $(Q_{\beta})_{\beta \geq 0}$ reflected at the origin. We use a probabilistic approach based on the continued fraction theory previously introduced

Comparison theorem and stability under perturbation of transition rate matrices for regimeswitching processes J. Appl. Probab. (IF 1.0) Pub Date : 20230914
Jinghai ShaoA comparison theorem for statedependent regimeswitching diffusion processes is established, which enables us to pathwisecontrol the evolution of the statedependent switching component simply by Markov chains. Moreover, a sharp estimate on the stability of Markovian regimeswitching processes under the perturbation of transition rate matrices is provided. Our approach is based on elaborate constructions

Strong convergence of peaks over a threshold J. Appl. Probab. (IF 1.0) Pub Date : 20230823
Simone A. Padoan, Stefano RizzelliExtreme 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

Normal and stable approximation to subgraph counts in superpositions of Bernoulli random graphs J. Appl. Probab. (IF 1.0) Pub Date : 20230818
Mindaugas Bloznelis, Joona Karjalainen, Lasse LeskeläReal 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

Reliability analyses of linear twodimensional consecutive ktype systems J. Appl. Probab. (IF 1.0) Pub Date : 20230814
He Yi, Narayanaswamy Balakrishnan, Xiang LiIn this paper, several linear twodimensional consecutive ktype systems are studied, which include the linear connected(k, r)outof $(m,n)\colon\! F$ system and the linear lconnected(k, r)outof $(m,n)\colon\! F$ 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

Stopping problems with an unknown state J. Appl. Probab. (IF 1.0) Pub Date : 20230809
Erik Ekström, Yuqiong WangWe 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 twosource

Chase–escape in dynamic devicetodevice networks J. Appl. Probab. (IF 1.0) Pub Date : 20230807
Elie Cali, Alexander Hinsen, Benedikt Jahnel, JeanPhilippe WaryWe feature results on global survival and extinction of an infection in a multilayer 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

Heavytraffic limits for parallel singleserver queues with randomly split Hawkes arrival processes J. Appl. Probab. (IF 1.0) Pub Date : 20230807
Bo Li, Guodong PangWe consider parallel singleserver 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 diffusionscaled queueing and workload processes converge to a multidimensional reflected

The proportion of triangles in a class of anisotropic Poisson line tessellations J. Appl. Probab. (IF 1.0) Pub Date : 20230807
Nils Heerten, Julia Krecklenberg, Christoph ThäleStationary 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 socalled Poisson line tessellation. The focus of this paper is to determine the proportion of triangles in such tessellations, or equivalently

Duality theory for exponential utilitybased hedging in the Almgren–Chriss model J. Appl. Probab. (IF 1.0) Pub Date : 20230803
Yan DolinskyIn 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 utilitybased hedging in the Bachelier model. For European contingent claims with a quadratic payoff, we compute the optimal trading strategy

On the joint survival probability of two collaborating firms J. Appl. Probab. (IF 1.0) Pub Date : 20230801
Stefan Ankirchner, Robert Hesse, Maike KleinWe 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

Phase transition for the generalized twocommunity stochastic block model J. Appl. Probab. (IF 1.0) Pub Date : 20230731
Sunmin Lee, Ji Oon LeeWe study the problem of detecting the community structure from the generalized stochastic block model with two communities (G2SBM). 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 G2SBM. For specific models, such as a hidden community model and an unbalanced stochastic block

Characterization of the optimal average cost in Markov decision chains driven by a riskseeking controller J. Appl. Probab. (IF 1.0) Pub Date : 20230721
Rolando CavazosCadena, Hugo CruzSuárez, Raúl MontesdeOcaThis 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 longrun average criterion as measured by a riskseeking decision maker with constant risksensitivity. Besides standard continuity–compactness conditions, the framework of the paper is determined by the following conditions: (i) the state

An elementary approach to the inverse firstpassagetime problem for softkilled Brownian motion J. Appl. Probab. (IF 1.0) Pub Date : 20230704
Alexander Klump, Martin KolbWe prove existence and uniqueness for the inversefirstpassage time problem for softkilled 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.

Optimal coupling of jumpy Brownian motion on the circle J. Appl. Probab. (IF 1.0) Pub Date : 20230704
Stephen B. Connor, Roberta MerliConsider 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 coadapted

Weakly interacting oscillators on dense random graphs J. Appl. Probab. (IF 1.0) Pub Date : 20230630
Gianmarco Bet, Fabio Coppini, Francesca Romana NardiWe consider a class of weakly interacting particle systems of meanfield 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

Differences between Lyapunov exponents for the simple random walk in Bernoulli potentials J. Appl. Probab. (IF 1.0) Pub Date : 20230623
Naoki KubotaWe consider the simple random walk on the ddimensional lattice $\mathbb{Z}^d$ ($d \geq 1$), traveling in potentials which are Bernoullidistributed. The socalled 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

Informationtheoretic convergence of extreme values to the Gumbel distribution J. Appl. Probab. (IF 1.0) Pub Date : 20230621
Oliver JohnsonWe show how convergence to the Gumbel distribution in an extreme value setting can be understood in an informationtheoretic 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

Monotonicity of implied volatility for perpetual put options J. Appl. Probab. (IF 1.0) Pub Date : 20230619
Erik Ekström, Ebba MellquistWe 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.

Explosion of continuousstate branching processes with competition in a Lévy environment J. Appl. Probab. (IF 1.0) Pub Date : 20230609
Rugang Ma, Xiaowen ZhouWe find sufficient conditions on explosion/nonexplosion for continuousstate branching processes with competition in a Lévy random environment. In particular, we identify the necessary and sufficient conditions on explosion/nonexplosion when the competition function is a power function and the Lévy measure of the associated branching mechanism is stable.

On relevation redundancy to coherent systems at component and system levels J. Appl. Probab. (IF 1.0) Pub Date : 20230609
Chen Li, Xiaohu LiRecently, 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

On a wider class of prior distributions for graphical models J. Appl. Probab. (IF 1.0) Pub Date : 20230608
Abhinav Natarajan, Willem van den Boom, Kristoforus Bryant Odang, Maria de IorioGaussian 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

Extrema of a multinomial assignment process J. Appl. Probab. (IF 1.0) Pub Date : 20230606
Mikhail Lifshits, Gilles MordantWe 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.

Tail variance allocation, Shapley value, and the majorization problem J. Appl. Probab. (IF 1.0) Pub Date : 20230606
Marcello Galeotti, Giovanni RabittiWith a focus on the risk contribution in a portofolio of dependent risks, ColiniBaldeschi 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 closedform expressions for the Shapley values for the tail variance game and we analyze the vector majorization

Exact convergence analysis for metropolis–hastings independence samplers in Wasserstein distances J. Appl. Probab. (IF 1.0) Pub Date : 20230605
Austin Brown, Galin L. JonesUnder 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 worstcase 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

Moderate deviations inequalities for Gaussian process regression J. Appl. Probab. (IF 1.0) Pub Date : 20230605
Jialin Li, Ilya O. RyzhovGaussian 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

Extropy: Characterizations and dynamic versions J. Appl. Probab. (IF 1.0) Pub Date : 20230602
Abdolsaeed Toomaj, Majid Hashempour, Narayanaswamy BalakrishnanSeveral 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

A confirmation of a conjecture on Feldman’s twoarmed bandit problem J. Appl. Probab. (IF 1.0) Pub Date : 20230526
Zengjing Chen, Yiwei Lin, Jichen ZhangThe myopic strategy is one of the most important strategies when studying bandit problems. In 2018, Nouiehed and Ross put forward a conjecture about Feldman’s bandit problem (J. Appl. Prob. (2018) 55, 318–324). They proposed that for Bernoulli twoarmed bandit problems, the myopic strategy stochastically maximizes the number of wins. In this paper we consider the twoarmed bandit problem with more

The winner takes it all but one J. Appl. Probab. (IF 1.0) Pub Date : 20230526
Maria Deijfen, Remco van der Hofstad, Matteo SfragaraWe study competing first passage percolation on graphs generated by the configuration model with infinitemean degrees. Initially, two uniformly chosen vertices are infected with a type 1 and type 2 infection, respectively, and the infection then spreads via nearest neighbors in the graph. The time it takes for the type 1 (resp. 2) infection to traverse an edge e is given by a random variable $X_1(e)$

A branching random walk in the presence of a hard wall J. Appl. Probab. (IF 1.0) Pub Date : 20230522
Rishideep RoyWe consider a branching random walk on a dary tree of height n ($n \in \mathbb{N}$), in the presence of a hard wall which restricts each value to be positive, where d is a natural number satisfying $d\geqslant2$. We consider the behaviour of Gaussian processes with longrange interactions, for example the discrete Gaussian free field, under the condition that it is positive on a large subset of vertices

A firstpassageplace problem for integrated diffusion processes J. Appl. Probab. (IF 1.0) Pub Date : 20230522
Mario LefebvreLet ${\mathrm{d}} X(t) = Y(t) \, {\mathrm{d}} t$, where Y(t) is a onedimensional diffusion process, and let $\tau(x,y)$ be the first time the process (X(t), Y(t)), starting from (x, y), leaves a subset of the first quadrant. The problem of computing the probability $p(x,y)\,:\!=\, \mathbb{P}[X(\tau(x,y))=0]$ is considered. The Laplace transform of the function p(x, y) is obtained in important particular

Kalikow decomposition for counting processes with stochastic intensity and application to simulation algorithms J. Appl. Probab. (IF 1.0) Pub Date : 20230519
Tien Cuong Phi, Eva Löcherbach, Patricia ReynaudBouretWe propose a new Kalikow decomposition for continuoustime multivariate counting processes, on potentially infinite networks. We prove the existence of such a decomposition in various cases. This decomposition allows us to derive simulation algorithms that hold either for stationary processes with potentially infinite network but bounded intensities, or for processes with unbounded intensities in a

Averaging for slow–fast piecewise deterministic Markov processes with an attractive boundary J. Appl. Probab. (IF 1.0) Pub Date : 20230519
Alexandre GénadotIn this paper we consider the problem of averaging for a class of piecewise deterministic Markov processes (PDMPs) whose dynamic is constrained by the presence of a boundary. On reaching the boundary, the process is forced to jump away from it. We assume that this boundary is attractive for the process in question in the sense that its averaged flow is not tangent to it. Our averaging result relies

Exponential control of the trajectories of iterated function systems with application to semistrong GARCH models J. Appl. Probab. (IF 1.0) Pub Date : 20230515
Baye Matar KandjiWe establish new results on the strictly stationary solution to an iterated function system. When the driving sequence is stationary and ergodic, though not independent, the strictly stationary solution may admit no moment but we show an exponential control of the trajectories. We exploit these results to prove, under mild conditions, the consistency of the quasimaximum likelihood estimator of GARCH(p