Related papers: Large Deviations for Stochastic Porous Media Equat…
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 study the large deviation principle (LDP) for obstacle problems governed by a T-monotone operator and small multiplicative stochastic reaction. Our approach relies on a combination of new sufficient condition to prove LDP…
By employing a new class of pseudo-differential operators introduced in a previous work, we establish a novel monotonicity formula for the fractional Laplacian $|\nabla_x|^\alpha$ in $\mathbb{R}^n$, with $n \geq 2$ and $\alpha \in [1,2)$,…
The purpose of this paper is to establish the Donsker-Varadhan type large deviations principle (LDP) for the two-dimensional stochastic Navier-Stokes system. The main novelty is that the noise is assumed to be highly degenerate in the…
We study the cubic weakly nonlinear Schr\"odinger equation with randomized spatially quasi-periodic initial data in higher dimensions. Under a polynomial decay assumption in Fourier space, we establish a {\em Large Deviations Principle} for…
The paper is devoted to studying the asymptotics of the family $(\mu^\varepsilon)$ of stationary measures of the Markov process generated by the flow of stochastic 2D Navier-Stokes equation with smooth white noise. By using the large…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
In this paper, we first provide a criterion on uniform large deviation principles (ULDP) of stochastic differential equations under Lyapunov conditions on the coefficients, which can be applied to stochastic systems with coefficients of…
In this work, a stochastic representation based on a physical transport principle is proposed to account for mesoscale eddy effects on the large-scale oceanic circulation. This stochastic framework arises from a decomposition of the…
We introduce a definition of the fractional Laplacian $(-\Delta)^{s(\cdot)}$ with spatially variable order $s:\Omega\to [0,1]$ and study the solvability of the associated Poisson problem on a bounded domain $\Omega$. The initial motivation…
We establish a general theory of optimal strong error estimation for numerical approximations of a second-order parabolic stochastic partial differential equation with monotone drift driven by a multiplicative infinite-dimensional Wiener…
In this paper, we study concentration phenomena of zero-noise limits of invariant measures for stochastic differential equations defined on $\mathbb{R}^d$ with locally Lipschitz continuous coefficients and more than one ergodic state. Under…
In this paper, we establish large deviation principle for the strong solution of a doubly nonlinear PDE driven by small multiplicative Brownian noise. Motononicity arguments and the weak convergence approach have been exploited in the…
In this paper, we establish a large deviation principle for stochastic models of two-dimensional second grade fluids driven by L\'evy noise. The weak convergence method introduced by Budhiraja, Dupuis and Maroulas in [5] plays a key role.
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
Motivated by Applied Physics and Photonics studies of random resonators, we study in the stochastic part of this paper random acoustic operators in non-smooth bounded domains $G \subset \mathbb{R}^d$ and introduce m-dissipative impedance…
We are concerned with a nonlinear nonautonomous model represented by an equation describing the dynamics of an age-structured population diffusing in a space habitat $O,$ governed by local Lipschitz vital factors and by a stochastic…
We consider stochastic nonlinear Schrodinger equations driven by an additive noise. The noise is fractional in time with Hurst parameter H in (0,1). It is also colored in space and the space correlation operator is assumed to be nuclear. We…
In this paper we establish the large deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity both for small noise and for short time. The proof for large deviation principle is based on…
In this paper we establish the large deviation principle for the stochastic quasi-geostrophic equation in the subcritical case with small multiplicative noise. The proof is mainly based on the stochastic control and weak convergence…