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Noise-induced transitions between multistable states happen in a multitude of systems, such as species extinction in biology, protein folding, or tipping points in climate science. Large deviation theory is the rigorous language to describe…

Probability · Mathematics 2024-09-27 Paolo Bernuzzi , Tobias Grafke

In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…

Dynamical Systems · Mathematics 2017-09-15 Getachew K. Befekadu

We present a large deviation principle for some stochastic evolution equations with jumps which depend on two small parameters, when the viscosity parameter {\epsilon} tends to zero more quickly than the homogenization's one…

Dynamical Systems · Mathematics 2019-10-29 C. Manga , A. Aman , A. Coulibaly , A. Diédhiou

Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {P_n} be a sequence of transition matrices on a…

Probability · Mathematics 2007-05-23 Zach Dietz , Sunder Sethuraman

We prove a large deviation principle for the slow-fast rough differential equations under the controlled rough path framework. The driver rough paths are lifted from the mixed fractional Brownian motion with Hurst parameter $H\in…

Probability · Mathematics 2025-02-05 Xiaoyu Yang , Yong Xu

In this paper, we consider asymptotic behaviors of multiscale multivalued stochastic systems with small noises. First of all, for general, fully coupled systems for multivalued stochastic differential equations of slow and fast motions with…

Probability · Mathematics 2025-09-30 Huijie Qiao

We prove a large-deviation principle (LDP) for the sample paths of jump Markov processes in the small noise limit when, possibly, all the jump rates vanish uniformly, but slowly enough, in a region of the state space. We further discuss the…

Probability · Mathematics 2021-02-26 Andrea Agazzi , Luisa Andreis , Robert I. A. Patterson , D. R. Michiel Renger

We study a Schilder-type large deviation principle for sticky-reflected Brownian motion with boundary diffusion, both at the static and sample path level in the short-time limit. A sharp transition for the rate function occurs, depending on…

Analysis of PDEs · Mathematics 2025-01-22 Jean-Baptiste Casteras , Leonard Monsaingeon , Luca Nenna

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

The Large Deviation Principle is established for stochastic models defined by past-dependent non linear recursions with small noise. In the Markov case we use the result to obtain an explicit expression for the asymptotics of exit time.

Probability · Mathematics 2007-05-23 F. Klebaner , R. Liptser

The aim of this paper is to investigate the large deviations for a class of slow-fast mean-field diffusions, which extends some existing results to the case where the laws of fast process are also involved in the slow component. Due to the…

Probability · Mathematics 2026-04-28 Wei Hong , Wei Liu , Shiyuan Yang

We establish a large deviation principle for the empirical measure process associated with a general class of finite-state mean field interacting particle systems with Lipschitz continuous transition rates that satisfy a certain ergodicity…

Probability · Mathematics 2016-01-26 Paul Dupuis , Kavita Ramanan , Wei Wu

The large deviation principle is established for the distributions of a class of generalized stochastic porous media equations for both small noise and short time.

Probability · Mathematics 2007-05-23 Michael Röckner , Feng-Yu Wang , Liming Wu

In this paper, we study the diffusion approximation for slow-fast stochastic differential equations with state-dependent switching, where the slow component $X^{\varepsilon}$ is the solution of a stochastic differential equation with…

Probability · Mathematics 2025-03-12 Xiaobin Sun , Jue Wang , Yingchao Xie

We provide an explicit rigorous derivation of a diffusion limit - a stochastic differential equation with additive noise - from a deterministic skew-product flow. This flow is assumed to exhibit time-scale separation and has the form of a…

Dynamical Systems · Mathematics 2015-05-27 I. Melbourne , A. M. Stuart

The asymptotic analysis of a class of stochastic partial differential equations (SPDEs) with fully locally monotone coefficients covering a large variety of physical systems, a wide class of quasilinear SPDEs and a good number of fluid…

Probability · Mathematics 2022-12-13 Ankit Kumar , Manil T. Mohan

We introduce order-based diffusion processes as the solutions to multidimensional stochastic differential equations, with drift coefficient depending only on the ordering of the coordinates of the process and diffusion matrix proportional…

Probability · Mathematics 2014-03-11 Benjamin Jourdain , Julien Reygner

We present large deviations estimates in the supremum norm for a system of independent random walks superposed with a birth-and-death dynamics evolving on the discrete torus with $N$ sites. The scaling limit considered is the so-called…

Probability · Mathematics 2021-02-26 Tertuliano Franco , Luana A. Gurgel , Bernardo N. B. de Lima

We consider a system of stochastic interacting particles in $\mathbb{R}^d$ and we describe large deviations asymptotics in a joint mean-field and small-noise limit. Precisely, a large deviations principle (LDP) is established for the…

Probability · Mathematics 2020-11-17 Carlo Orrieri

The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…

Statistical Mechanics · Physics 2012-03-01 Hugo Touchette