Related papers: Uniform large deviations and metastability of rand…
The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations…
We investigate three types of averaging principles and the normal deviation for multi-scale stochastic differential equations (in short, SDEs) with polynomial nonlinearity. More specifically, we first demonstrate the strong convergence of…
Stochastic partial differential equations driven by Poisson random measures (PRM) have been proposed as models for many different physical systems, where they are viewed as a refinement of a corresponding noiseless partial differential…
Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of…
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 this paper, we establish the large deviation principles for stochastic porous media equations driven by time-dependent multiplicative noise on $\sigma$-finite measure space $(E,\mathcal{B}(E),\mu)$, and the Laplacian replaced by a…
We study deviation of U-statistics when samples have heavy-tailed distribution so the kernel of the U-statistic does not have bounded exponential moments at any positive point. We obtain an exponential upper bound for the tail of the…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
We prove that the statistical properties of random perturbations of a nonuniformly hyperbolic diffeomorphism are described by a finite number of stationary measures. We also give necessary and sufficient conditions for the stochastic…
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…
We prove the validity of a small noise large deviation principle for the family of invariant measures $\{\mu_\epsilon\}_{\epsilon>0} $ associated to the one dimensional stochastic Allen-Cahn equation with inhomogeneous Dirichlet boundary…
We study the convergence in total variation and $V$-norm of discretization schemes of the underdamped Langevin dynamics. Such algorithms are very popular and commonly used in molecular dynamics and computational statistics to…
We study a class of stochastic differential equations with non-Lipschitzian coefficients.A unique strong solution is obtained and a large deviation principle of Freidln-Wentzell type has been established.
We unify and extend the semigroup and the PDE approaches to stochastic maximal regularity of time-dependent semilinear parabolic problems with noise given by a cylindrical Brownian motion. We treat random coefficients that are only…
Timesteppers constitute a powerful tool in modern computational science and engineering. Although they are typically used to advance the system forward in time, they can also be viewed as nonlinear mappings that implicitly encode steady…
In this paper we prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
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 recover the Donsker-Varadhan large deviations principle (LDP) for the empirical measure of a continuous time Markov chain on a countable (finite or infinite) state space from the joint LDP for the empirical measure and the empirical flow…
We consider generalized Bayesian inference on stochastic processes and dynamical systems with potentially long-range dependency. Given a sequence of observations, a class of parametrized model processes with a prior distribution, and a loss…