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Exit Times for a Discrete Markov Additive Process J. Theor. Probab. (IF 0.8) Pub Date : 2024-03-17 Zbigniew Palmowski, Lewis Ramsden, Apostolos D. Papaioannou
In this paper, we consider (upward skip-free) discrete-time and discrete-space Markov additive chains (MACs) and develop the theory for the so-called \(\widetilde{{\textbf {W}}}\) and \(\widetilde{{\textbf {Z}}}\) scale matrices, which are shown to play a vital role in the determination of a number of exit problems and related fluctuation identities. The theory developed in this fully discrete set-up
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Hausdorff Measure and Uniform Dimension for Space-Time Anisotropic Gaussian Random Fields J. Theor. Probab. (IF 0.8) Pub Date : 2024-03-15 Weijie Yuan, Zhenlong Chen
Let \(X=\{ X(t), t\in \mathbb {R}^{N}\} \) be a centered space-time anisotropic Gaussian random field in \(\mathbb {R}^d\) with stationary increments, where the components \(X_{i}(i=1,\ldots ,d)\) are independent but distributed differently. Under certain conditions, we not only give the Hausdorff dimension of the graph sets of X in the asymmetric metric in the recurrent case, but also determine the
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The Voter Model with a Slow Membrane J. Theor. Probab. (IF 0.8) Pub Date : 2024-03-13 Linjie Zhao, Xiaofeng Xue
We introduce the voter model on the infinite integer lattice with a slow membrane and investigate its hydrodynamic behavior and nonequilibrium fluctuations. The voter model is one of the classical interacting particle systems with state space \(\{0,1\}^{\mathbb Z^d}\). In our model, a voter adopts one of its neighbors’ opinion at rate one except for neighbors crossing the hyperplane \(\{x:x_1 = 1/2\}\)
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Rough Differential Equations Containing Path-Dependent Bounded Variation Terms J. Theor. Probab. (IF 0.8) Pub Date : 2024-03-08 Shigeki Aida
We consider rough differential equations whose coefficients contain path-dependent bounded variation terms and prove the existence and a priori estimate of solutions. These equations include classical path-dependent stochastic differential equations containing running maximum processes and normal reflection terms. We apply these results to determine the topological support of the solution processes
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Homogenization of a Multivariate Diffusion with Semipermeable Interfaces J. Theor. Probab. (IF 0.8) Pub Date : 2024-03-07
Abstract We study the homogenization problem for a system of stochastic differential equations with local time terms that models a multivariate diffusion in the presence of semipermeable hyperplane interfaces with oblique penetration. We show that this system has a unique weak solution and determine its weak limit as the distances between the interfaces converge to zero. In the limit, the singular
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Precise Tail Behaviour of Some Dirichlet Series J. Theor. Probab. (IF 0.8) Pub Date : 2024-03-05 Alexander Iksanov, Vitali Wachtel
Let \(\eta _1\), \(\eta _2,\ldots \) be independent copies of a random variable \(\eta \) with zero mean and finite variance which is bounded from the right, that is, \(\eta \le b\) almost surely for some \(b>0\). Considering different types of the asymptotic behaviour of the probability \(\mathbb {P}\{\eta \in [b-x,b]\}\) as \(x\rightarrow 0+\), we derive precise tail asymptotics of the random Dirichlet
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Multivariate Random Fields Evolving Temporally Over Hyperbolic Spaces J. Theor. Probab. (IF 0.8) Pub Date : 2024-02-28 Anatoliy Malyarenko, Emilio Porcu
Gaussian random fields are completely characterised by their mean value and covariance function. Random fields on hyperbolic spaces have been studied to a limited extent only, namely for the case of scalar-valued fields that are not evolving over time. This paper challenges the problem of the second-order characteristics of multivariate (vector-valued) random fields that evolve temporally over hyperbolic
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General Transfer Formula for Stochastic Integral with Respect to Multifractional Brownian Motion J. Theor. Probab. (IF 0.8) Pub Date : 2024-03-01 Christian Bender, Joachim Lebovits, Jacques Lévy Véhel
Abstract In this work we show how results from stochastic integration with respect to multifractional Brownian motion (mBm) can be simply deduced from results of stochastic integration with respect to fractional Brownian motion (fBm), by using a “Transfer Principle”. To illustrate this fact, we prove an Itô formula for integral with respect to mBm by deriving it from Itô formula for integral with respect
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Probability and Moment Inequalities for Additive Functionals of Geometrically Ergodic Markov Chains J. Theor. Probab. (IF 0.8) Pub Date : 2024-02-18 Alain Durmus, Eric Moulines, Alexey Naumov, Sergey Samsonov
In this paper, we establish moment and Bernstein-type inequalities for additive functionals of geometrically ergodic Markov chains. These inequalities extend the corresponding inequalities for independent random variables. Our conditions cover Markov chains converging geometrically to the stationary distribution either in weighted total variation norm or in weighted Wasserstein distances. Our inequalities
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Invariant Measures for the Nonlinear Stochastic Heat Equation with No Drift Term J. Theor. Probab. (IF 0.8) Pub Date : 2024-02-15 Le Chen, Nicholas Eisenberg
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Non-uniqueness Phase of Percolation on Reflection Groups in $${\mathbb {H}^3}$$ J. Theor. Probab. (IF 0.8) Pub Date : 2024-02-15 Jan Czajkowski
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Fractional Skellam Process of Order k J. Theor. Probab. (IF 0.8) Pub Date : 2024-02-12
Abstract We introduce and study a fractional version of the Skellam process of order k by time-changing it with an independent inverse stable subordinator. We call it the fractional Skellam process of order k (FSPoK). An integral representation for its one-dimensional distributions and their governing system of fractional differential equations are obtained. We derive the probability generating function
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Waiting Time for a Small Subcollection in the Coupon Collector Problem with Universal Coupon J. Theor. Probab. (IF 0.8) Pub Date : 2024-01-21 Jelena Jocković, Bojana Todić
We consider a generalization of the classical coupon collector problem, where the set of available coupons consists of standard coupons (which can be part of the collection), and two coupons with special purposes: one that speeds up the collection process and one that slows it down. We obtain several asymptotic results related to the expectation and the variance of the waiting time until a portion
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A Note on Transience of Generalized Multi-Dimensional Excited Random Walks J. Theor. Probab. (IF 0.8) Pub Date : 2024-01-11 Rodrigo B. Alves, Giulio Iacobelli, Glauco Valle
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On Convergence of the Uniform Norm and Approximation for Stochastic Processes from the Space $${\textbf{F}}_\psi (\Omega )$$ J. Theor. Probab. (IF 0.8) Pub Date : 2023-12-20 Iryna Rozora, Yurii Mlavets, Olga Vasylyk, Volodymyr Polishchuk
In this paper, we consider random variables and stochastic processes from the space \({\textbf{F}}_\psi (\Omega )\) and study approximation problems for such processes. The method of series decomposition of a stochastic process from \({\textbf{F}}_\psi (\Omega )\) is used to find an approximating process called a model. The rate of convergence of the model to the process in the uniform norm is investigated
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The Time-Dependent Symbol of a Non-homogeneous Itô Process and Corresponding Maximal Inequalities J. Theor. Probab. (IF 0.8) Pub Date : 2023-12-19
Abstract The probabilistic symbol is defined as the right-hand side derivative at time zero of the characteristic functions corresponding to the one-dimensional marginals of a time-homogeneous stochastic process. As described in various contributions to this topic, the symbol contains crucial information concerning the process. When leaving time-homogeneity behind, a modification of the symbol by inserting
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The Moduli of Continuity for Operator Fractional Brownian Motion J. Theor. Probab. (IF 0.8) Pub Date : 2023-12-15 Wensheng Wang
The almost-sure sample path behavior of the operator fractional Brownian motion with exponent D, including multivariate fractional Brownian motion, is investigated. In particular, the global and the local moduli of continuity of the sample paths are established. These results show that the global and the local moduli of continuity of the sample paths are completely determined by the real parts of the
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Strong Approximations for a Class of Dependent Random Variables with Semi-Exponential Tails J. Theor. Probab. (IF 0.8) Pub Date : 2023-12-06 Christophe Cuny, Jérôme Dedecker, Florence Merlevède
We give rates of convergence in the almost sure invariance principle for sums of dependent random variables with semi-exponential tails, whose coupling coefficients decrease at a sub-exponential rate. We show that the rates in the strong invariance principle are in powers of \(\log n\). We apply our results to iid products of random matrices.
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Sojourn Times of Gaussian Processes with Random Parameters J. Theor. Probab. (IF 0.8) Pub Date : 2023-11-25 Goran Popivoda, Siniša Stamatović
In this paper, we investigate the sojourn times of conditionally Gaussian processes, i.e., the sojourns of \(\xi (t)+\lambda -\zeta \,t^\beta \) and \(\xi (t)(\lambda -\zeta \,t^\beta )\), \(t\in [0, T],\ T>0\), where \(\xi \) is a Gaussian zero-mean stationary process and \(\lambda \) and \(\zeta \) are random variables independent of \(\xi (\cdot )\), and \(\beta >0\) is a constant.
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Limiting Distributions for a Class of Super-Brownian Motions with Spatially Dependent Branching Mechanisms J. Theor. Probab. (IF 0.8) Pub Date : 2023-11-25 Yan-Xia Ren, Ting Yang
In this paper, we consider a large class of super-Brownian motions in \({\mathbb {R}}\) with spatially dependent branching mechanisms. We establish the almost sure growth rate of the mass located outside a time-dependent interval \((-\delta t,\delta t)\) for \(\delta >0\). The growth rate is given in terms of the principal eigenvalue \(\lambda _{1}\) of the Schrödinger-type operator associated with
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Coupled McKean–Vlasov Equations Over Convex Domains J. Theor. Probab. (IF 0.8) Pub Date : 2023-11-18 Guangying Lv, Wei Wang, Jinlong Wei
In this paper, the reflected McKean–Vlasov diffusion ov a convex domain is studied. We first establish the well-posedness of a coupled system of nonlinear stochastic differential equations via a fixed point theorem which is similar to that for partial differential equations. Moreover, the reason why we make different assumptions on drift and cross terms is given. Then, the propagation of chaos for
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Existence and Uniqueness of Denumerable Markov Processes with Instantaneous States J. Theor. Probab. (IF 0.8) Pub Date : 2023-11-18 Xiaohan Wu, Anyue Chen, Junping Li
Based on the resolvent decomposition theorems presented very recently by Chen (J Theor Probab 33:2089–2118, 2020), in this paper we focus on investigating the fundamental problems of existence and uniqueness criteria for Denumerable Markov Processes with finitely many instantaneous states. Some elegant sufficient and necessary conditions are obtained for this less-investigated topic. A few important
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On Markov Intertwining Relations and Primal Conditioning J. Theor. Probab. (IF 0.8) Pub Date : 2023-11-16 Marc Arnaudon, Koléhè Coulibaly-Pasquier, Laurent Miclo
Given an intertwining relation between two finite Markov chains, we investigate how it can be transformed by conditioning the primal Markov chain to stay in a proper subset. A natural assumption on the underlying link kernel is put forward. The three classical examples of discrete Pitman, top-to-random shuffle and absorbed birth-and-death chain intertwinings serve as illustrations.
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Limit Theorem for Self-intersection Local Time Derivative of Multidimensional Fractional Brownian Motion J. Theor. Probab. (IF 0.8) Pub Date : 2023-11-09 Qian Yu, Xianye Yu
The existence condition \(H<1/d\) for first-order derivative of self-intersection local time for \(d\ge 3\) dimensional fractional Brownian motion was obtained in Yu (J Theoret Probab 34(4):1749–1774, 2021). In this paper, we establish a limit theorem under the nonexistence critical condition \(H=1/d\).
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A Robust $$\alpha $$ -Stable Central Limit Theorem Under Sublinear Expectation without Integrability Condition J. Theor. Probab. (IF 0.8) Pub Date : 2023-11-03 Lianzi Jiang, Gechun Liang
This article fills a gap in the literature by relaxing the integrability condition for the robust \(\alpha \)-stable central limit theorem under sublinear expectation. Specifically, for \(\alpha \in (0,1]\), we prove that the normalized sums of i.i.d. non-integrable random variables \(\big \{n^{-\frac{1}{\alpha }}\sum _{i=1}^{n}Z_{i}\big \}_{n=1}^{\infty }\) converge in law to \({\tilde{\zeta }}_{1}\)
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Shannon–McMillan–Breiman Theorem Along Almost Geodesics in Negatively Curved Groups J. Theor. Probab. (IF 0.8) Pub Date : 2023-11-02 Amos Nevo, Felix Pogorzelski
Consider a non-elementary Gromov-hyperbolic group \(\Gamma \) with a suitable invariant hyperbolic metric, and an ergodic probability measure preserving (p.m.p.) action on \((X,\mu )\). We construct special increasing sequences of finite subsets \(F_n(y)\subset \Gamma \), with \((Y,\nu )\) a suitable probability space, with the following properties. Given any countable partition \(\mathcal {P}\) of
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Laws of Large Numbers for Weighted Sums of Independent Random Variables: A Game of Mass J. Theor. Probab. (IF 0.8) Pub Date : 2023-11-01 Luca Avena, Conrado da Costa
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On the Local Time of Anisotropic Random Walk on $$\mathbb Z^2$$ J. Theor. Probab. (IF 0.8) Pub Date : 2023-10-31 Endre Csáki, Antónia Földes
We study the local time of the anisotropic random walk on the two-dimensional lattice \(\mathbb {Z}^2\), by establishing the exact asymptotic behavior of the N-step return probability to the origin.
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A Theory of Singular Values for Finite Free Probability J. Theor. Probab. (IF 0.8) Pub Date : 2023-10-29 Aurelien Gribinski
We introduce a finite version of free probability for rectangular matrices that amounts to operations on singular values of polynomials. This study is motivated by the companion papers Gribinski (J Comb Theory. arXiv:1904.11552; Existence and polynomial time construction of biregular, bipartite Ramanujan graphs of all degrees. arXiv:2108.02534) , as well as the corresponding paper dealing with the
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Some Properties of Markov chains on the Free Group $${\mathbb {F}}_2$$ J. Theor. Probab. (IF 0.8) Pub Date : 2023-10-18 Antoine Goldsborough, Stefanie Zbinden
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Lower Deviation for the Supremum of the Support of Super-Brownian Motion J. Theor. Probab. (IF 0.8) Pub Date : 2023-10-19 Yan-Xia Ren, Renming Song, Rui Zhang
We study the asymptotic behavior of the supremum \(M_t\) of the support of a supercritical super-Brownian motion. In our recent paper (Ren et al. in Stoch Proc Appl 137:1–34, 2021), we showed that, under some conditions, \(M_t-m(t)\) converges in distribution to a randomly shifted Gumbel random variable, where \(m(t)=c_0t-c_1\log t\). In the same paper, we also studied the upper large deviation of
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Cutpoints of (1,2) and (2,1) Random Walks on the Lattice of Positive Half Line J. Theor. Probab. (IF 0.8) Pub Date : 2023-10-13 Lanlan Tang, Hua-Ming Wang
In this paper, we study (1,2) and (2,1) random walks in spatially inhomogeneous environments on the lattice of positive half line. We assume that the transition probabilities at site n are asymptotically constant as \(n\rightarrow \infty .\) We get some elaborate limit behaviors of various escape probabilities and hitting probabilities of the walk. Such observations and some delicate analysis of continued
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Green Function for an Asymptotically Stable Random Walk in a Half Space J. Theor. Probab. (IF 0.8) Pub Date : 2023-09-29 Denis Denisov, Vitali Wachtel
We consider an asymptotically stable multidimensional random walk \(S(n)=(S_1(n),\ldots , S_d(n) )\). For every vector \(x=(x_1\ldots ,x_d)\) with \(x_1\ge 0\), let \(\tau _x:=\min \{n>0: x_{1}+S_1(n)\le 0\}\) be the first time the random walk \(x+S(n)\) leaves the upper half space. We obtain the asymptotics of \(p_n(x,y):= {\textbf{P}}(x+S(n) \in y+\Delta , \tau _x>n)\) as n tends to infinity, where
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General Mean Reflected Backward Stochastic Differential Equations J. Theor. Probab. (IF 0.8) Pub Date : 2023-09-25 Ying Hu, Remi Moreau, Falei Wang
The present paper is devoted to the study of backward stochastic differential equations (BSDEs) with mean reflection formulated by Briand et al. (Ann Appl Probab 28(1):482–510, 2018). We investigate the solvability of a generalized mean reflected BSDE, whose driver also depends on the distribution of solution term Y. Using a fixed-point argument, BMO martingale theory and the \(\theta \)-method, we
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Joint Sum-and-Max Limit for a Class of Long-Range Dependent Processes with Heavy Tails J. Theor. Probab. (IF 0.8) Pub Date : 2023-09-25 Shuyang Bai, He Tang
We consider a class of stationary processes exhibiting both long-range dependence and heavy tails. Separate limit theorems for sums and for extremes have been established recently in the literature with novel objects appearing in the limits. In this article, we establish the joint sum-and-max limit theorems for this class of processes. In the finite-variance case, the limit consists of two independent
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The Distributions of the Mean of Random Vectors with Fixed Marginal Distribution J. Theor. Probab. (IF 0.8) Pub Date : 2023-09-25 Andrzej Komisarski, Jacques Labuschagne
Using recent results concerning non-uniqueness of the center of the mix for completely mixable probability distributions, we obtain the following result: For each\(d\in {\mathbb {N}}\) and each non-empty bounded Borel set \(B\subset {\mathbb {R}}^d\), there exists a d-dimensional probability distribution \(\varvec{\mu }\) satisfying the following: For each \(n\ge 3\) and each probability distribution
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Explicit Approximation of Invariant Measure for Stochastic Delay Differential Equations with the Nonlinear Diffusion Term J. Theor. Probab. (IF 0.8) Pub Date : 2023-09-22 Xiaoyue Li, Xuerong Mao, Guoting Song
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Asymptotic Properties of Extremal Markov Processes Driven by Kendall Convolution J. Theor. Probab. (IF 0.8) Pub Date : 2023-09-05 Marek Arendarczyk, Barbara Jasiulis-Gołdyn, Edward Omey
This paper is devoted to the analysis of the finite-dimensional distributions and asymptotic behavior of extremal Markov processes connected with the Kendall convolution. In particular, we provide general formulas for the finite dimensional distributions of the random walk driven by the Kendall convolution for a large class of step size distributions. Moreover, we prove limit theorems for random walks
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Random Transpositions on Contingency Tables J. Theor. Probab. (IF 0.8) Pub Date : 2023-09-04 Mackenzie Simper
The space of contingency tables with n total entries and fixed row and column sums is in bijection with parabolic double cosets of \(S_n\). Via this correspondence, the uniform distribution on \(S_n\) induces the Fisher–Yates distribution on contingency tables, which is classical for its use in the chi-squared test for independence. This paper studies the Markov chain on contingency tables induced
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Normal Approximation of Kabanov–Skorohod Integrals on Poisson Spaces J. Theor. Probab. (IF 0.8) Pub Date : 2023-09-01 G. Last, I. Molchanov, M. Schulte
We consider the normal approximation of Kabanov–Skorohod integrals on a general Poisson space. Our bounds are for the Wasserstein and the Kolmogorov distance and involve only difference operators of the integrand of the Kabanov–Skorohod integral. The proofs rely on the Malliavin–Stein method and, in particular, on multiple applications of integration by parts formulae. As examples, we study some linear
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Multilinear Smoothing and Local Well-Posedness of a Stochastic Quadratic Nonlinear Schrödinger Equation J. Theor. Probab. (IF 0.8) Pub Date : 2023-08-29 Nicolas Schaeffer
In this article, we study a d-dimensional stochastic quadratic nonlinear Schrödinger equation (SNLS), driven by a fractional derivative (of order \(-\alpha <0\)) of a space-time white noise: $$\begin{aligned} \left\{ \begin{array}{l} i\partial _t u-\Delta u= \rho ^2 |u|^2 +\langle \nabla \rangle ^{-\alpha }\dot{W}, \quad t\in [0,T], \, x\in {\mathbb {R}}^d,\\ u_0=\phi \, , \end{array}\right. \end{aligned}$$
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Bifractional Brownian Motions on Metric Spaces J. Theor. Probab. (IF 0.8) Pub Date : 2023-08-25 Chunsheng Ma
Fractional and bifractional Brownian motions can be defined on a metric space if the associated metric or distance function is conditionally negative definite (or of negative type). This paper introduces several forms of scalar or vector bifractional Brownian motions on various metric spaces and presents their properties. A metric space of particular interest is the arccos-quasi-quadratic metric space
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Harmonic Moments and Large Deviations for the Markov Branching Process with Immigration J. Theor. Probab. (IF 0.8) Pub Date : 2023-08-14 Liuyan Li, Junping Li
Let \(\{X_t;t\ge 0\}\) be a Markov branching process with immigration, in which each particle has exponential lifetime distribution with parameter a and offspring law \(\{p_k;k=0,1,2,\ldots \}\). The time interval of immigration follows an exponential distribution with parameter \(\theta \). Let \(p_0=0\) and \(\lambda :=a(\sum _{k=1}^{\infty }kp_k-1)<\infty \). In this paper, we investigate the large
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Sub-exponentiality in Statistical Exponential Models J. Theor. Probab. (IF 0.8) Pub Date : 2023-08-12 Barbara Trivellato
Improvements in the study of nonparametric maximal exponential models built on Orlicz spaces are proposed. By exploiting the notion of sub-exponential random variable, we give theoretical results which provide a clearer insight into the structure of these models. The explicit constants we obtain when changing the law of Orlicz spaces centered at connected densities allow us to derive uniform bounds
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Reflected Backward Stochastic Differential Equations Driven by G-Brownian Motion Under Monotonicity Condition J. Theor. Probab. (IF 0.8) Pub Date : 2023-08-02 Bingjun Wang, Hongjun Gao, Mingxia Yuan, Qingkun Xiao
In this paper, we construct an approximation sequence by a smoothing method for continuous functions; then, we prove that there exists a unique solution to reflected backward stochastic differential equations driven by G-Brownian motion when the coefficients do not satisfy the Lipschitz condition. Moreover, we prove a comparison theorem.
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Cutoff on Trees is Rare J. Theor. Probab. (IF 0.8) Pub Date : 2023-07-31 Nina Gantert, Evita Nestoridi, Dominik Schmid
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Analysis of the Limiting Spectral Distribution of Large-dimensional General Information-Plus-Noise-Type Matrices J. Theor. Probab. (IF 0.8) Pub Date : 2023-07-28 Huanchao Zhou, Jiang Hu, Zhidong Bai, Jack W. Silverstein
In this paper, we derive the analytical behavior of the limiting spectral distribution of non-central covariance matrices of the “general information-plus-noise" type, as studied in Zhou (JTP 36:1203–1226, 2023). Through the equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic wherever it is positive
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A Strong Convergence Rate of the Averaging Principle for Two-Time-Scale Forward-Backward Stochastic Differential Equations J. Theor. Probab. (IF 0.8) Pub Date : 2023-07-29 Jie Xu, Qiqi Lian
In this paper, we study the strong convergence rate of the averaging principle of two-time-scale forward-backward stochastic differential equations (FBSDEs, for short). First, we present the well-posedness of the objective equations and then we give some a priori estimates for FBSDEs, backward stochastic auxiliary equations and backward stochastic averaged equations. Second, a strong convergence rate
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Spectrum of Lévy–Khintchine Random Laplacian Matrices J. Theor. Probab. (IF 0.8) Pub Date : 2023-07-26 Andrew Campbell, Sean O’Rourke
We consider the spectrum of random Laplacian matrices of the form \(L_n=A_n-D_n\) where \(A_n\) is a real symmetric random matrix and \(D_n\) is a diagonal matrix whose entries are equal to the corresponding row sums of \(A_n\). If \(A_n\) is a Wigner matrix with entries in the domain of attraction of a Gaussian distribution, the empirical spectral measure of \(L_n\) is known to converge to the free
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Convergence of Martingales with Jumps on Submanifolds of Euclidean Spaces and its Applications to Harmonic Maps J. Theor. Probab. (IF 0.8) Pub Date : 2023-07-10 Fumiya Okazaki
Martingales with jumps on Riemannian manifolds and harmonic maps with respect to Markov processes are discussed in this paper. Discontinuous martingales on manifolds were introduced in Picard (Séminaire de Probabilités de Strasbourg 25:196–219, 1991). We obtain results about the convergence of martingales with finite quadratic variations on Riemannian submanifolds of higher-dimensional Euclidean space
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On Sharp Rate of Convergence for Discretization of Integrals Driven by Fractional Brownian Motions and Related Processes with Discontinuous Integrands J. Theor. Probab. (IF 0.8) Pub Date : 2023-07-10 Ehsan Azmoodeh, Pauliina Ilmonen, Nourhan Shafik, Tommi Sottinen, Lauri Viitasaari
We consider equidistant approximations of stochastic integrals driven by Hölder continuous Gaussian processes of order \(H>\frac{1}{2}\) with discontinuous integrands involving bounded variation functions. We give exact rate of convergence in the \(L^1\)-distance and provide examples with different drivers. It turns out that the exact rate of convergence is proportional to \(n^{1-2H}\), which is twice
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On Conditioning Brownian Particles to Coalesce J. Theor. Probab. (IF 0.8) Pub Date : 2023-07-08 Vitalii Konarovskyi, Victor Marx
We introduce the notion of a conditional distribution to a zero-probability event in a given direction of approximation and prove that the conditional distribution of a family of independent Brownian particles to the event that their paths coalesce after the meeting coincides with the law of a modified massive Arratia flow, defined in Konarovskyi (Ann Probab 45(5):3293–3335, 2017. https://doi.org/10
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Gradient Flows on Graphons: Existence, Convergence, Continuity Equations J. Theor. Probab. (IF 0.8) Pub Date : 2023-07-03 Sewoong Oh, Soumik Pal, Raghav Somani, Raghavendra Tripathi
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Generalized Backward Doubly Stochastic Differential Equations Driven by Lévy Processes with Discontinuous and Linear Growth Coefficients J. Theor. Probab. (IF 0.8) Pub Date : 2023-06-30 Jean-Marc Owo, Auguste Aman
This paper deals with generalized backward doubly stochastic differential equations driven by a Lévy process (GBDSDEL, in short). Under left or right continuous and linear growth conditions, we prove the existence of minimal (resp. maximal) solutions.
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Scaling Limits of Slim and Fat Trees J. Theor. Probab. (IF 0.8) Pub Date : 2023-06-23 Vladislav Kargin
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On the Analysis of Ait-Sahalia-Type Model for Rough Volatility Modelling J. Theor. Probab. (IF 0.8) Pub Date : 2023-06-13 Emmanuel Coffie, Xuerong Mao, Frank Proske
Fractional Brownian motion with Hurst parameter \(H<\frac{1}{2}\) is used widely, for instance, to describe ‘rough’ volatility data in finance. In this paper, we examine a generalised Ait-Sahalia-type model driven by a fractional Brownian motion with \(H<\frac{1}{2}\) and establish theoretical properties such as an existence-and-uniqueness theorem, regularity in the sense of Malliavin differentiability
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Exponential Behaviour of Nonlinear Fractional Schrödinger Evolution Equation with Complex Potential and Poisson Jumps J. Theor. Probab. (IF 0.8) Pub Date : 2023-06-07 N. Durga, P. Muthukumar
This paper aims to investigate stochastic fractional Schrödinger evolution equations with potential and Poisson jumps in Hilbert space. The solvability of the proposed system is established by using fractional calculus, semigroup theory, Krasnoselskii’s fixed point theorems and stochastic analysis. Furthermore, sufficient conditions are formulated and proved to assure that the mild solution decays
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Fractional Poisson Processes of Order k and Beyond J. Theor. Probab. (IF 0.8) Pub Date : 2023-06-07 Neha Gupta, Arun Kumar
In this article, we introduce fractional Poisson fields of order k in n-dimensional Euclidean space of positive real valued vectors. We also work on time-fractional Poisson process of order k, space-fractional Poisson processes of order k and a tempered version of time-space fractional Poisson processes of order k. We discuss generalized fractional Poisson processes of order k in terms of Bernstein
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Derivative of Multiple Self-intersection Local Time for Fractional Brownian Motion J. Theor. Probab. (IF 0.8) Pub Date : 2023-05-24 Jingjun Guo, Cuiyun Zhang, Aiqin Ma
We consider existence and the Hölder continuity condition in the spatial variable for the derivative of multiple self-intersection local time for fractional Brownian motion. Moreover, under the existence condition, we study its smoothness in the sense of Meyer–Watanabe.