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Our purpose is to prove central limit theorem for countable nonhomogeneous Markov chain under the condition of uniform convergence of transition probability matrices for countable nonhomogeneous Markov chain in Ces\`aro sense. Furthermore,…

Probability · Mathematics 2020-10-15 Mingzhou Xu , Yunzheng Ding , Yongzheng Zhou

In this article, we establish the Freidlin-Wentzell type large deviation principle and central limit theorem for stochastic fractional conservation laws with small multiplicative noise in kinetic formulation framework. The weak convergence…

Probability · Mathematics 2023-06-08 Soumya Ranjan Behera , Ananta K. Majee

The wave speed of a stochastic wave equation driven by Riesz noise on the unbounded multidimensional spatial domain is estimated based on discrete measurements. Central limit theorems for second-order variations of the observations in…

Statistics Theory · Mathematics 2026-02-05 Anton Tiepner , Mathias Trabs , Eric Ziebell

The goal of this paper is to study the Moderate Deviation Principle (MDP) for a system of stochastic reaction-diffusion equations with a time-scale separation in slow and fast components and small noise in the slow component. Based on weak…

Probability · Mathematics 2022-02-03 Ioannis Gasteratos , Michael Salins , Konstantinos Spiliopoulos

This paper studies quantitative deviation bounds for statistical ensembles evolving under the one-parameter flow of a nearly integrable Hamiltonian system. Combining Nekhoroshev-type stability estimates with phase-mixing arguments, we…

Dynamical Systems · Mathematics 2026-02-23 Xinyu Liu , Yong Li

We consider the nodal length $L(\lambda)$ of the restriction to a ball of radius $r_\lambda$ of a {\it Gaussian pullback monochromatic random wave} of parameter $\lambda>0$ associated with a Riemann surface $(\mathcal M,g)$ without…

Probability · Mathematics 2020-05-15 Gauthier Dierickx , Ivan Nourdin , Giovanni Peccati , Maurizia Rossi

In the paper [25], written in collaboration with Gesine Reinert, we proved a universality principle for the Gaussian Wiener chaos. In the present work, we aim at providing an original example of application of this principle in the…

Probability · Mathematics 2010-02-08 Ivan Nourdin , Giovanni Peccati

This is basically a polished presentation for Sections 1,2 of arXiv:0801.1050. The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and…

Probability · Mathematics 2016-12-28 Boris Tsirelson

In this paper, we prove a central limit theorem and a moderate deviation principle for a perturbed stochastic Cahn-Hilliard equation defined on [0, T]x [0, \pi]^d, with d \in {1,2,3}. This equation is driven by a space-time white noise. The…

Probability · Mathematics 2018-10-15 Ruinan Li , Xinyu Wang

In a paper from 1995, Wormald gave general criteria for certain parameters in a family of discrete random processes to converge to the solution of a system of differential equations. Based on this method, we show that if some further…

Probability · Mathematics 2009-06-24 Taral Guldahl Seierstad

This paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise which are observed at high frequency. Our method generalizes the pre-averaging approach (see [Bernoulli 15 (2009) 634--658,…

Statistics Theory · Mathematics 2010-10-05 Jean Jacod , Mark Podolskij , Mathias Vetter

For a L\'evy basis $L$ on $\mathbb{R}^d$ and a suitable kernel function $f:\mathbb{R}^d \to \mathbb{R}$, consider the continuous spatial moving average field $X=(X_t)_{t\in \mathbb{R}^d}$ defined by $X_t = \int_{\mathbb{R}^d} f(t-s) \,…

Probability · Mathematics 2021-08-02 David Berger

In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain Burgers' equation and the stochastic reaction-diffusion equation. The weak…

Probability · Mathematics 2018-11-21 Shulan Hu , Ruinan Li , Xinyu Wang

We consider Berry's random planar wave model (1977), and prove spatial functional limit theorems - in the high-energy limit - for discretized and truncated versions of the random field obtained by restricting its nodal length to rectangular…

Probability · Mathematics 2023-05-24 Massimo Notarnicola , Giovanni Peccati , Anna Vidotto

We use a new method via $p$-Wasserstein bounds to prove Cram\'er-type moderate deviations in (multivariate) normal approximations. In the classical setting that $W$ is a standardized sum of $n$ independent and identically distributed…

Probability · Mathematics 2022-05-27 Xiao Fang , Yuta Koike

The work concerns deviation estimates for multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the large deviation principle for them by the weak convergence approach. Then the central limit theorem for them…

Probability · Mathematics 2022-08-10 Kun Fang , Huijie Qiao

In this paper we study Strichartz estimates for dispersive equations which are defined by radially symmetric pseudo-differential operators, and of which initial data belongs to spaces of Sobolev type defined in spherical coordinates. We…

Analysis of PDEs · Mathematics 2012-12-06 Yonggeun Cho , Sanghyuk Lee

We show that for local alternatives to uniformity which are determined by a sequence of square integrable densities the moderate deviation (MD) theorem for the corresponding Neyman-Pearson statistic does not hold in the full range for all…

Statistics Theory · Mathematics 2020-03-27 Tadeusz Inglot

The term \emph{moderate deviations} is often used in the literature to mean a class of large deviation principles that, in some sense, fill the gap between a convergence in probability to zero (governed by a large deviation principle) and a…

Probability · Mathematics 2022-07-15 Rita Giuliano , Claudio Macci

The purpose of the present paper is to establish explicit bounds on moderate deviation probabilities for a rather general class of geometric functionals enjoying the stabilization property, under Poisson input and the assumption of a…

Probability · Mathematics 2015-03-17 Peter Eichelsbacher , Martin Raic , Tomasz Schreiber