相关论文: Stable Central Limit Theorems for Super Ornstein-U…

Suppose that $\{X_t,\,t\ge0\}$ is a non-stationary Markov process, taking values in a Polish metric space $E$. We prove the law of large numbers and central limit theorem for an additive functional of the form $\int_0^T\psi(X_s)ds$,…

We study dynamical systems arising as time-dependent compositions of Pomeau-Manneville-type intermittent maps. We establish central limit theorems for appropriately scaled and centered Birkhoff-like partial sums, with estimates on the rate…

We study the stability of the mesoscopic fluctuations of certain orthogonal polynomial ensembles on the real line utilizing the recurrence relation of the associated orthogonal polynomials. We prove that under a sparse enough decaying…

In this article, we quantify the functional convergence of the rescaled random walk with heavy tails to a stable process.This generalizes the Generalized Central Limit Theorem for stable random variables infinite dimension. We show that…

We consider the class of simple Brown-Resnick max-stable processes whose spectral processes are continuous exponential martingales. We develop the asymptotic theory for the realized power variations of these max-stable processes, that is,…

In this paper we consider an Ornstein-Uhlenbeck (OU) process $(M(t))_{t\geqslant 0}$ whose parameters are determined by an external Markov process $(X(t))_{t\geqslant 0}$ on a finite state space $\{1,\ldots,d\}$; this process is usually…

We provide a sufficient characterization for subsets $\mathcal{A}$ of the polynomial ring $\mathbb{F}_q[t]$ for which partial sums of Steinhaus random multiplicative functions approach a complex standard normal distribution. This extends…

The so-called "supOU" processes, namely the superpositions of Ornstein-Uhlenbeck type processes are stationary processes for which one can specify separately the marginal distribution and the dependence structure. They can have finite or…

We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper establishes the following results: (a) Functional central limit theorems for the…

In the context of non-equilibrium statistical physics, the entropy production rate is an important concept to describe how far a specific state of a system is from its equilibrium state. In this paper, we establish a central limit theorem…

Consider a supercritical Crump--Mode--Jagers process $(\mathcal Z_t^{\varphi})_{t \geq 0}$ counted with a random characteristic $\varphi$. Nerman's celebrated law of large numbers [Z. Wahrsch. Verw. Gebiete 57, 365--395, 1981] states that,…

We prove a functional central limit theorem for integrals $\int_W f(X(t))\, dt$, where $(X(t))_{t\in\mathbb{R}^d}$ is a stationary mixing random field and the stochastic process is indexed by the function $f$, as the integration domain $W$…

We study a class of discrete-time random walks in $\mathbb{R}^d$ whose conditional drift decays polynomially in time and grows polynomially with the distance from the origin to the current position. This class is related to several models…

Our aim in this paper is to investigate the asymptotic behavior of solutions of the perturbed linear fractional differential system. We show that if the original linear autonomous system is asymptotically stable then under the action of…

We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We focus…

In this paper, we focus on studying central limit theorems for functionals of some specific stationary random processes. In classical probability theory, it is well-known that for non-linear functionals of stationary Gaussian sequences, we…

Consider a particle moving through a random medium, which consists of spherical obstacles, randomly distributed in R^d. The particle is accelerated by a constant external field; when colliding with an obstacle, the particle inelastically…

This paper studies the existence and global stability of generalized Ornstein-Uhlenbeck process for affine stochastic functional differential equations. Various very basic and important properties are established. In the applications, we…

We consider a class of subcritical superprocesses $(X_t)_{t\geq 0}$ with general spatial motions and general branching mechanisms. We study the asymptotic behaviors of $\mathbf Q_{t,r}$, the distribution of $X_t$ conditioned on $X_{t+r}$…

A central limit theorem is proved for some strictly stationary sequences of random variables that satisfy certain mixing conditions and are subjected to the "shrinking operators" $U_r(x):=[\max\{|x|-r,0\}]\cdot x/|x|,\ r \ge 0$. For…