Related papers: Large deviations for slow-fast stochastic partial …
We establish a large deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, the large deviation principle is derived for super-Brownian…
We establish the large deviation principle for stochastic differential equations with averaging in the case when all coefficients of the fast component depend on the slow one, including diffusion.
Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any…
In this paper, we establish a large deviation principle for the conservative stochastic partial differential equations, whose solutions are related to stochastic differential equations with interaction. The weak convergence method and the…
The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…
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.
This study focuses on large deviation principles for fully coupled multiscale multivalued stochastic systems, in which the slow component is governed by a multivalued stochastic differential equation and the fast component is described by a…
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…
In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The…
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 here a simple method for computing the large deviation of long time average for stochastic jump processes. We show that the computation of the rate function can be reduced to that of a partial differential equation governing the…
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…
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…
In this paper we consider the Allen-Cahn equation perturbed by a stochastic flux term and prove a large deviation principle. Using an associated stochastic flow of diffeomorphisms the equation can be transformed to a parabolic partial…
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…
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…
A large deviation function mathematically characterizes the statistical property of atypical events. Recently, in non-equilibrium statistical mechanics, large deviation functions have been used to describe universal laws such as the…
The paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of…
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 present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square…