The functional iterated logarithm law for stochastic processes represented by multiple Wiener integrals

Abstract

In a previous paper the authors obtained a functional law of the iterated logarithm for a class of self-similar processes\(\bar X\) with stationary increments, which are represented by multiple Wiener integrals. This result is extended to a certain class of processes represented by multiple Wiener integrals which converge to\(\bar X\) with an appropriate normalization. As an application a functional log log law for nonlinear functionals of some stationary Gaussian processes is given.