Moderate Deviation Principle for a Class of SPDEs

TL;DR

This paper proves the moderate deviation principle for solutions of certain SPDEs with non-Lipschitz coefficients and applies it to models like super-Brownian motion and Fleming-Viot process.

Contribution

It introduces the moderate deviation principle for a class of SPDEs with non-Lipschitz coefficients and applies it to key population models.

Findings

Established the moderate deviation principle for the solutions of the SPDEs.

Derived the moderate deviation principle for super-Brownian motion.

Derived the moderate deviation principle for Fleming-Viot process.

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 Fleming-Viot process.