The existence and smoothness of self-intersection local time for a class of Gaussian processes

In this paper sufficient conditions for the existence and smoothness of the self-intersection local time of a class of Gaussian processes are given in the sense of Meyer-Watanabe through L-2 convergence and Wiener chaos expansion. Let X be a centered Gaussian process, whose canonical metric E[(X(t) - X(s)(2))] is commensurate with sigma(2)(|t - s|), where sigma(center dot) is continuous, increasing and concave. If integral(T)(0) 1/sigma(gamma) d gamma < infinity, then the self-intersection local time of the Gaussian process exists, and if integral(T)(0) (sigma(gamma))(-3/2) d gamma < infinity, the self-intersection local time of the Gaussian process is smooth in the sense of Meyer-Watanabe.