The Law of the Iterated Logarithm for a Class of SPDEs

TL;DR

This paper proves the law of the iterated logarithm for certain SPDEs and population models, extending classical results and establishing new probabilistic limit laws for these stochastic systems.

Contribution

It introduces the first proof of Strassen's LIL for a class of SPDEs and applies it to super-Brownian motion and Fleming-Viot processes, extending classical LIL results.

Findings

Established Strassen's LIL for a class of SPDEs

Applied LIL to super-Brownian motion and Fleming-Viot process

Proved classical LIL for these stochastic models

Abstract

After establishing the moderate deviation principle by the Classical Azencott method, we prove the Strassen's compact law of the iterated logarithm (LIL) for a class of stochastic partial differential equations (SPDEs). As an application, we obtain this type of LIL for two population models known as super-Brownian motion and Fleming-Viot process. In addition, the classical LIL is shown for the class of SPDEs and the two population models.