The law of the iterated logarithm for a class of SPDEs

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.