Related papers: On large deviations in the averaging principle for…
We prove pathwise large deviation principles of slow variables in slow-fast systems in the limit of time-scale separation tending to infinity. In the limit regime we consider, the convergence of the slow variable to its deterministic limit…
This paper is devoted to proving the strong averaging principle for slow-fast stochastic partial differential equations with locally monotone coefficients, where the slow component is a stochastic partial differential equations with locally…
We prove the averaging principle for a class of stochastic systems. The slow component is solution to a fractional differential equation, which is coupled with a fast component considered as solution to an ergodic stochastic differential…
We study the validity of an averaging principle for a slow-fast system of stochastic reaction diffusion equations. We assume here that the coefficients of the fast equation depend on time, so that the classical formulation of the averaging…
We investigate the large deviation principle (LDP) of the stationary solutions of stochastic functional differential equations (SFDEs) with infinite delay under small random perturbation. First, we demonstrate the existence and uniqueness…
Using Zvonkin's transform and the Poisson equation in $R^d$ with a parameter, we prove the averaging principle for stochastic differential equations with time-dependent H\"older continuous coefficients. Sharp convergence rates with order…
A large deviation principle is established for a general class of stochastic flows in the small noise limit. This result is then applied to a Bayesian formulation of an image matching problem, and an approximate maximum likelihood property…
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…
In this paper, using Zvonkin type transform, the large deviation principle is proved for stochastic differential equations with Dini continuous drifts, where the existed methods for large deviation principle are unavailable. The method and…
We prove a large deviation principle for stochastic differential equations driven by semimartingales, with additive controls. Conditions are given in terms of characteristics of driven semimartingales, so that if the noise-control pairs…
We present the validity of stochastic averaging principle for non-autonomous slow-fast stochastic differential equations (SDEs) whose fast motions admit random periodic solutions. Our investigation is motivated by some problems arising from…
The large deviation principle in the small noise limit is derived for solutions of possibly degenerate It\^o stochastic differential equations with predictable coefficients, which may depend also on the large deviation parameter. The result…
This work focuses on multivalued stochastic differential equations with jumps. First, by employing the weak convergence approach, we establish the Freidlin-Wentzell uniform large deviation principle and the Dembo-Zeitouni uniform large…
The Freidlin-Wentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. As examples, the main results are applied to derive the large…
In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.
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…
In this paper, we establish a large deviation principle for a type of stochastic partial differential equations (SPDEs) with locally monotone coefficients driven by L\'evy noise. The weak convergence method plays an important role.
In this paper we develop the large deviations principle and a rigorous mathematical framework for asymptotically efficient importance sampling schemes for general, fully dependent systems of stochastic differential equations of slow and…
This paper establishes a Freidlin-Wentzell large deviation principle for stochastic differential equations(SDEs) under locally weak monotonicity conditions and Lyapunov conditions. We illustrate the main result of the paper by showing that…
We establish a large deviation principle for a reflected Poisson driven SDE. Our motivation is to study in a forthcoming paper the problem of exit of such a process from the basin of attraction of a locally stable equilibrium associated…