Hiroshi Oodaira

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

SummaryIn a previous paper the authors obtained a functional law of the iterated logarithm for a class of self-similar processes

Functional central limit theorems for strictly stationary processes satisfyinc the strong mixing condition

\bar X

The law of the iterated logarithm for self-similar processes represented by multiple wiener integrals

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

A FUNCTIONAL LAW OF THE ITERATED LOGARITHM FOR SAMPLE SEQUENCES

\bar X

A renewal theorem on (J, X)-processes

with an appropriate normalization. As an application a functional log log law for nonlinear functionals of some stationary Gaussian processes is given.