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This article is concerned with moderate deviation principles of a general class of mean eld type interacting particle models. We discuss functional moderate deviations of the occupation measures for both the strong -topology on the space of…

Probability · Mathematics 2012-04-17 Pierre Del Moral , Shulan Hu , Liming Wu

Cram\'er's moderate deviations give a quantitative estimate for the relative error of the normal approximation and provide theoretical justifications for many estimator used in statistics. In this paper, we establish self-normalized…

Probability · Mathematics 2025-03-03 Xiequan Fan , Qi-Man Shao

The main aim of this paper is to study the moderate deviation principle for McKean-Vlasov stochastic differential equations with multiple scales. Specifically, we are interested in the asymptotic estimates of the deviation processes…

Probability · Mathematics 2024-09-20 Wei Hong , Ge Li , Shihu Li

In this paper, moderate deviations for normal approximation of functionals over infinitely many Rademacher random variables are derived. They are based on a bound for the Kolmogorov distance between a general Rademacher functional and a…

Probability · Mathematics 2024-06-12 Marius Butzek , Peter Eichelsbacher , Benedikt Rednoß

Consider the stochastic differential equation in $\rr^d$ dX^{\e}_t&=b(X^{\e}_t)dt+\sqrt{\e}\sigma(X^\e_t)dB_t X^{\e}_0&=x_0,\quad x_0\in\rr^d$ where $b:\rr^d\to\rr^d$ is $C^1$ such that $<x,b(x)> \leq C(1+|x|^2)$, $\sigma:\rr^d\to…

Probability · Mathematics 2026-04-14 Yutao ma , Ran Wang , Liming Wu

This work studies a two-time-scale functional system given by two jump-diffusions under the scale separation by a small parameter $\varepsilon \rightarrow 0$. The coefficients of the equations that govern the dynamics of the system depend…

Probability · Mathematics 2022-07-15 André de Oliveira Gomes , Pedro Catuogno

In this paper, we prove the moderate deviations principle (MDP) for a general system of slow-fast dynamics. We provide a unified approach, based on weak convergence ideas and stochastic control arguments, that cover both the averaging and…

Probability · Mathematics 2017-06-02 Matthew R. Morse , Konstantinos Spiliopoulos

We establish Cram\'er-type moderate deviation theorems for sums of locally dependent random variables and combinatorial central limit theorems. Under some mild exponential moment conditions, optimal error bounds and convergence ranges are…

Probability · Mathematics 2021-12-22 Song-Hao Liu , Zhuo-Song Zhang

We establish a Cram\'er-type moderate deviation result for self-normalized sums of weakly dependent random variables, where the moment requirement is much weaker than the non-self-normalized counterpart. The range of the moderate deviation…

Statistics Theory · Mathematics 2014-09-15 Xiaohong Chen , Qi-Man Shao , Wei Biao Wu

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

We consider a stable but nearly unstable autoregressive process of any order. The bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with spectral radius $\rho(A_{n}) < 1$ satisfying…

Statistics Theory · Mathematics 2019-10-17 Frédéric Proïa

The purpose of this paper is to investigate the deviation inequalities and the moderate deviation principle of the least squares estimators of the unknown parameters of general $p$th-order bifurcating autoregressive processes, under…

Probability · Mathematics 2012-04-12 Hacène Djellout , Valère Bitseki Penda

This note provides a tool to infer moderate deviations principles for specific random variables from deviations principles for their Hubbard-Stratonovich transforms.

Probability · Mathematics 2012-10-03 Matthias Löwe , Raphael Meiners

The necessary and sufficient conditions for a function to be totally or partially separable are derived. It is shown that a function is totally separable if and only if each component of the gradient vector of depends only on the…

Numerical Analysis · Mathematics 2025-10-20 C. P. Viazminsky

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability of some random variables to a constant and a weak convergence…

Probability · Mathematics 2024-11-20 Rita Giuliano , Claudio Macci , Barbara Pacchiarotti

We present a general central limit theorem with simple, easy-to-check covariance-based sufficient conditions for triangular arrays of random vectors when all variables could be interdependent. The result is constructed from Stein's method,…

Moderate deviation principles for stochastic differential equations driven by a Poisson random measure (PRM) in finite and infinite dimensions are obtained. Proofs are based on a variational representation for expected values of positive…

Probability · Mathematics 2014-01-29 Amarjit Budhiraja , Paul Dupuis , Arnab Ganguly

In this paper, we investigate a stochastic approximation procedure $\left(X_n\right)_{n\ge 0}$ taking values in $R$. The process is adapted to a filtration $(F_n)_{n\ge 0}$ and satisfies the recursion…

Probability · Mathematics 2026-05-11 Jianan Shi , Qing Yin , Yu Miao

We investigate random walks in independent, identically distributed random sceneries under the assumption that the scenery variables satisfy Cramer's condition. We prove moderate deviation principles in dimensions two and larger, covering…

Probability · Mathematics 2007-05-23 Klaus Fleischmann , Peter Morters , Vitali Wachtel

We derive Cram\'{e}r type moderate deviations for stationary sequences of bounded random variables. Our results imply the moderate deviation principles and a Berry-Esseen bound. Applications to quantile coupling inequalities, functions of…

Probability · Mathematics 2019-07-04 Xiequan Fan