Strassen's law of the iterated logarithm for stochastic Volterra equations and applications

Abstract

We prove a version of Strassen's law of iterated logarithm (LIL) for a family of stochastic Volterra equation. Our approach is similar to that of Baldi [2], Large deviations and functional iterated logarithm law for diffusion processes for diffusion process. As applications of our results, we firstly prove Strassen's LIL for hyperbolic stochastic partial differential equation and secondly we give a version of Strassen's LIL for fractional Brownian motion (fBm) and its local time for Hurst parameter