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We investigate the Large Deviations properties of bootstrapped empirical measure with exchangeable weights. Our main result shows in great generality how the resulting rate function combines the LD properties of both the sample weights and…

Probability · Mathematics 2011-10-24 José Trashorras , Olivier Wintenberger

A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a…

Probability · Mathematics 2017-05-09 Amarjit Budhiraja , Paul Dupuis , Arnab Ganguly

The large deviations theory for heavy-tailed processes has seen significant advances in the recent past. In particular, Rhee et al. (2019) and Bazhba et al. (2020) established large deviation asymptotics at the sample-path level for L\'evy…

Probability · Mathematics 2024-10-29 Zhe Su , Chang-Han Rhee

The present paper is devoted to the large deviation principle (LDP), with particular emphasis on the regularity of the quasi-potential for densities of stationary and quasi-stationary distributions of randomly perturbed dynamical systems.…

Dynamical Systems · Mathematics 2025-06-24 Chenchen Mou , Weiwei Qi , Zhongwei Shen , Yingfei Yi

This paper deals with rare events in a general {interacting gas} at high temperature, by means of Large Deviations Principles. The main result is an LDP for the tagged empirical field, which features the competition of an energy term and an…

Probability · Mathematics 2025-06-17 David Padilla-Garza

In this paper we study empirical measures which can be thought as a decoupled version of the empirical measures generated by random matrices. We prove the large deviation principle with the rate function, which is finite only on product…

Probability · Mathematics 2007-05-23 Wlodek Bryc

In this work, we study the large deviation properties of random walk in a random environment on $\mathbb{Z}^d$ with $d\geq1$. We start with the quenched case, take the point of view of the particle, and prove the large deviation principle…

Probability · Mathematics 2008-09-09 Atilla Yilmaz

We prove large deviation principles (LDPs) for random matrices in the orthogonal group and Stiefel manifold, determining both the speed and good convex rate functions that are explicitly given in terms of certain log-determinants of…

Probability · Mathematics 2022-11-04 Zakhar Kabluchko , Joscha Prochno

A general approach to a broad class of asymptotic problems related to long-time influence of small perturbations, of both deterministic and stochastic type, is presented in the paper. The main characteristic of this influence is a limiting…

Probability · Mathematics 2020-10-06 Mark Freidlin

Moderate deviation principles for empirical measure processes associated with weakly interacting Markov processes are established. Two families of models are considered: the first corresponds to a system of interacting diffusions whereas…

Probability · Mathematics 2015-10-09 Amarjit Budhiraja , Ruoyu Wu

We consider a family of positive operator valued measures associated with representations of compact connected Lie groups. For many independent copies of a single state and a tensor power representation we show that the observed probability…

Mathematical Physics · Physics 2024-09-04 Alonso Botero , Matthias Christandl , Péter Vrana

Localized sufficient conditions for the large deviation principle of the given stochastic differential equations will be presented for stochastic differential equations with non-Lipschitzian and time-inhomogeneous coefficients, which is…

Probability · Mathematics 2014-04-08 Yunjiao Hu , Guangqiang Lan

Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which…

Probability · Mathematics 2021-08-03 Alain Durmus , Arnaud Guillin , Pierre Monmarché

This article discusses modelling of the tail of a multivariate distribution function by means of a large deviation principle (LDP), and its application to the estimation of the probability of a multivariate extreme event from a sample of n…

Statistics Theory · Mathematics 2017-02-23 Cees de Valk

We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…

Probability · Mathematics 2023-09-14 Amarjit Budhiraja , Pavlos Zoubouloglou

We consider probability measures on $A^N$, the set of sequences of symbols on a finite alphabet $A$ of length $N$, that give a weight to each sequence in terms of a collection of matrices with non-negative entries and having rows and…

Probability · Mathematics 2026-01-21 Davide Gabrielli , Federica Iacovissi

We consider the moment space $\mathcal{M}_n^{K}$ corresponding to $p \times p$ complex matrix measures defined on $K$ ($K=[0,1]$ or $K=\D$). We endow this set with the uniform law. We are mainly interested in large deviations principles…

Probability · Mathematics 2011-10-17 Fabrice Gamboa , Jan Nagel , Alain Rouault , Jens Wagener

For a $d-$regular random model, we assign to vertices $q-$state spins. From this model, we define the \emph{empirical co-operate measure}, which enumerates the number of co-operation between a given couple of spins, and \emph{ empirical…

Probability · Mathematics 2017-11-15 U. Ibrahim , A. Lotsi , K. Doku-Amponsah

Using the weak convergence approach, we prove the large deviation principle (LDP) for solutions to quasilinear stochastic evolution equations with small Gaussian noise in the critical variational setting, a recently developed general…

Probability · Mathematics 2026-02-23 Esmée Theewis , Mark Veraar

We establish a Large Deviations Principle for stochastic processes with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control problem and is proved to be good. The proof…

Probability · Mathematics 2010-12-14 Magdalena Kobylanski