相关论文: Central limit theorems and suppression of anomalou…

This article considers the statistical properties of L\'evy walks possessing a regular long-term linear scaling of the mean square displacement with time, for which the conditions of the classical Central Limit Theorem apply.…

We obtain sufficient conditions exlcuding the existence of non-trivial distribution sections of bundles over the boundary of symmetric spaces of negative curvature which are invariant with respect to a geometrically finite group of…

The main result of this paper is a general central limit theorem for distributions defined by certain renewal type equations. We apply this to weakly self-avoiding random walks. We give good error estimates and Gaussian tail estimates which…

We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central…

Heterogeneous media diffusion is often described using position-dependent diffusion coefficients and estimated indirectly through mean squared displacement in experiments. This approach may overlook other mechanisms and their interaction…

Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…

We consider a random walk $(Y_N)_{N\geq 0}$ on $\mathbb{R}^2$ generated by successively applying independent random isometries, drawn from a fixed measure $\mu$, to the point $0$. When the support of $\mu$ is finite and includes an…

We prove that a planar random walk with bounded increments and mean zero which is conditioned to stay in a cone converges weakly to the corresponding Brownian meander if and only if the tail distribution of the exit time from the cone is…

A novel probabilistic framework for modelling anomalous diffusion is presented. The resulting process is Markovian, non-homogeneous, non-stationary, non-ergodic, and state-dependent. The fundamental law governing this process is driven by…

Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of…

A central limit theorem for arrays of symmetric row-wise exchangeable random variables is presented. The result is valid for finite and infinite extendable and non-extendable sequences. Unlike most reported versions of the central limit…

In this paper we extend a central limit theorem of Peligrad for uniformly strong mixing random fields satisfying the Lindeberg condition in the absence of stationarity property. More precisely, we study the asymptotic normality of the…

We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…

The first aim of this paper is to wonder to what extent we can generalize the central limit theorem of Gordin [5] under the so-called L 1-projective criteria to ergodic stationary random fields when completely commuting filtrations are…

We study of the effect of weak noise on critical one dimensional maps; that is, maps with a renormalization theory. We establish a one dimensional central limit theorem for weak noises and obtain Berry--Esseen estimates for the rate of this…

We address the issue of the Central Limit Theorem for (both local and global) empirical measures of diffusions interacting on a possibly diluted Erd\H{o}s-R\'enyi graph. Special attention is given to the influence of initial condition (not…

We propose a Langevin equation for systems in an environment with nonuniform temperature. At odds with an older proposal, ours admits a locally Maxwellian steady state, local equipartition holds and for detailed-balanced (reversible)…

We prove a Berry-Esseen theorem, a local central limit theorem and (local) large and (global) moderate deviations principles for i.i.d. (uniformly) random non-uniformly expanding or hyperbolic maps with exponential first return times. Using…

This short note shows a limiting behavior of integrals of some centered antipersistent stationary infinitely divisible moving averages as the compact integration domain in $d\ge 1$ dimensions extends to the whole positive quadrant…

This paper establishes limit theorems and quantitative statistical stability for a class of piecewise partially hyperbolic maps that are not necessarily continuous nor locally invertible. By employing a flexible functional-analytic…