Moderate deviation principle for a class of stochastic partial differential equations

Abstract

We establish the moderate deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, we derive the moderate deviation principle for two important population models: super-Brownian motion and the Fleming-Viot process.

Some Exit Time Estimates for Super-Brownian Motion and Fleming-Viot Process

“…The distribution of gene types is studied in FVP making it a probability measure-valued process; whereas, SBM is a measure-valued process. For more information and background on these population models we refer the reader to [11,16,19,30].…”

Some exit times estimates for Super-Brownian motion and Fleming-Viot Process

“…The distribution of gene types is studied in FVP making it a probability measure-valued process; whereas, SBM is a measure-valued process. For more information and background on these population models we refer the reader to [11,16,19,30].…”

Central Limit Theorem And Moderate Deviation Principle For Inviscid Stochastic Burgers Equation

“…Further, Dong et al [15] considered the MDP for 2D Navier-Stokes equations driven by multiplicative Lévy noises in D([0, T ]; H) ∩ L 2 ([0, T ]; V). In view of the characterization of the super-Brownian motion (SBM) and the Fleming-Viot process (FVP), Fatheddin and Xiong [20] obtained MDP for those processes. Recently, the CLT and MDP for stochastic Burgers equation with viscosity term have been studied by several authors, see [4,35].…”