Related papers: A large deviation principle for nonlinear stochast…

We consider the damped nonlinear wave (NLW) equation driven by a spatially regular white noise. Assuming that the noise is non-degenerate in all Fourier modes, we establish a large deviations principle (LDP) for the occupation measures of…

We consider a stochastic wave equation in space dimension three driven by a noise white in time and with an absolutely continuous correlation measure given by the product of a smooth function and a Riesz kernel. Let $p_{t,x}(y)$ be the…

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…

In this paper, we establish a small time large deviation principles for the quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone.

Consider the non-linear stochastic fractional-diffusion equation \begin{eqnarray*} \left \{\begin{array}{lll} \frac{\partial}{\partial t}u(x,t)= -( \Delta)^{\alpha/2} u^m(x,t) + \sigma(u(x,t)) \dot{W}(x,t),\, x\in \mathbb{R}^d,t>0, u(x,0)=…

This work is devoted to the asymptotic analysis of high frequency wave propagation in random media with long-range dependence. We are interested in two asymptotic regimes, that we investigate simultaneously: the paraxial approximation,…

Fix $d\in\{1,2\}$, we consider a $d$-dimensional stochastic wave equation driven by a Gaussian noise, which is temporally white and colored in space such that the spatial correlation function is integrable and satisfies Dalang's condition.…

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.

The main objective of this paper is to demonstrate the uniform large deviation principle (UDLP) for the solutions of two-dimensional stochastic Navier-Stokes equations (SNSE) in the vorticity form when perturbed by two distinct types of…

In this article, we develop a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the limits of spherical integrals obtained in [46,47]. As examples, we obtain 1. 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…

The Laplace principle for the strong solution of the stochastic shell model of turbulence perturbed by Levy noise is established in a suitable Polish space using weak convergence approach. The large deviation principle is proved using the…

We consider a $d$-dimensional random field $u = \{u(t,x)\}$ that solves a non-linear system of stochastic wave equations in spatial dimensions $k \in \{1,2,3\}$, driven by a spatially homogeneous Gaussian noise that is white in time. We…

This paper attempts to obtain necessary and sufficient conditions to solve the parabolic Anderson model with fractional Gaussian noises: $\frac{\partial}{\partial t}u(t,x)=\frac{1}{2}\Delta u(t,x)+u(t,x)\dot{W}(t,x)$, where $ {W}(t,x)$ is…

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…

Consider the following stochastic partial differential equation, \begin{equation*} \partial_t u_t(x)= \mathcal{L}u_t(x)+ \xi\sigma (u_t(x)) \dot F(t,x), \end{equation*} where $\xi$ is a positive parameter and $\sigma$ is a globally…

In this paper, we consider a kind of fully coupled slow fast motion, in which the slow variable satisfies the non Lipschitz condition. We prove that the stochastic flow of the slow variable exists and moreover, satisfies the large deviation…

We consider nonlinear parabolic evolution equations of the form $\partial_{t}u=F(t,x,Du,D^{2}u) $, subject to noise of the form $H(x,Du) \circ dB$ where $H$ is linear in $Du$ and $\circ dB$ denotes the Stratonovich differential of a…

We study the time-fractional stochastic heat equation driven by time-space white noise with space dimension $d\in\mathbb{N}=\{1,2,...\}$ and the fractional time-derivative is the Caputo derivative of order $\alpha \in (0,2)$. We consider…

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…