Related papers: Large deviation principles for the stochastic quas…

We establish a microscopic convexity principle for nonlinear elliptic and parabolic partial differential equations in general form.

The main results in this paper concern large deviations for families of non-Gaussian processes obtained as suitable perturbations of continuous centered multivariate Gaussian processes which satisfy a large deviation principle. We present…

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…

The large deviation properties of equilibrium (reversible) lattice gases are mathematically reasonably well understood. Much less is known in non--equilibrium, namely for non reversible systems. In this paper we consider a simple example of…

This work is concerned with the large deviation principle for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion with Hurst parameter $H\in(\frac12,1)$. We adopt the weak convergence method…

The present paper focuses on the stochastic nonlinear Schrodinger equation with polynomial nonlinearity, and a zero-order (no derivatives involved) linear damping. Here, the random forcing term appears as a mix of a nonlinear noise in the…

Shot noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory and in the engineering sciences. In this work we prove a large deviation principle…

We study large deviations from the invariant measure for nonlinear Schr\"odinger equations with colored noises on determining modes. The proof is based on a new abstract criterion, inspired by [V. Jak\v{s}i\'{c} et al., Comm. Pure Appl.…

Over the last 50 years a steady stream of accounts have been written on the separation principle of stochastic control. Even in the context of the linear-quadratic regulator in continuous time with Gaussian white noise, subtle difficulties…

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…

In this paper we are concerned with the maximum principle for quasi-linear backward stochastic partial differential equations (BSPDEs for short) of parabolic type. We first prove the existence and uniqueness of the weak solution to…

The large deviations principles are established for a class of multidimensional degenerate stochastic differential equations with reflecting boundary conditions. The results include two cases where the initial conditions are adapted and…

We prove a Freidlin-Wentzell large deviation principle for general stochastic evolution equations with small perturbation multiplicative noises. In particular, our general result can be used to deal with a large class of quasi linear…

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…

This paper is concerned with the large deviation principle of the stochastic reaction-diffusion lattice systems defined on the N-dimensional integer set, where the nonlinear drift term is locally Lipschitz continuous with polynomial growth…

In this paper, a large deviation principle for the strong solution of the p-Laplace equation on unbounded domain driven by small multiplicative Brownian noise is established. The weak convergence approach and the localized time increment…

In this paper, we establish a central limit theorem (CLT) and the moderate deviation principles (MDP) for a class of semilinear stochastic partial differential equations driven by multiplicative noise on a bounded domain. The main results…

In this paper, we prove a central limit theorem and establish a moderate deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity. The proof for moderate deviation principle is based on…

In this paper, we provide a criterion on uniform large deviation principles (ULDP) for stochastic differential equations under locally weak monotone conditions and Lyapunov conditions, which can be applied to stochastic systems with…

Moderate deviation principle is achieved by the weak convergence approach for a stochastic Schr\"odinger type equation with linear drift term and noise driven by a $Q$-Wiener process. The central limit theorem is also shown for the equation…