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A Freidlin-Wentzell type large deviation principle is established for stochastic partial differential equations with slow and fast time-scales, where the slow component is a one-dimensional stochastic Burgers equation with small noise and the fast component is a stochastic reaction-diffusion equation. Our approach is via the weak convergence criterion developed in [3].
The present work deals with the global solvability as well as asymptotic analysis of stochastic generalized Burgers-Huxley (SGBH) equation perturbed by space-time white noise in a bounded interval of $mathbb{R}$. We first prove the existence of uniqu
We establish a central limit theorem and prove a moderate deviation principle for inviscid stochastic Burgers equation. Due to the lack of viscous term, this is done in the framework of kinetic solution. The weak convergence method and doubling variables method play a key role.
In this review we discuss the weak KPZ universality conjecture for a class of 1-d systems whose dynamics conserves one or more quantities. As a prototype example for the former case, we will focus on weakly asymmetric simple exclusion processes, for
We derive from a class of microscopic asymmetric interacting particle systems on ${mathbb Z}$, with long range jump rates of order $|cdot|^{-(1+alpha)}$ for $0<alpha<2$, different continuum fractional SPDEs. More specifically, we show the equilibrium
This paper is devoted to investigating the Freidlin-Wentzells large deviation principle for a class of McKean-Vlasov quasilinear SPDEs perturbed by small multiplicative noise. We adopt the variational framework and the modified weak convergence crite