GENERALIZED SELF INTERSECTION LOCAL TIME FOR A SUPERPROCESS OVER A STOCHASTIC FLOW

This paper examines the existence of the self-intersection local time for a superprocess over a stochastic flow in dimensions d ≤ 3, which through constructive methods, results in a Tanaka like representation. The superprocess over a stochastic flow is a superprocess with dependent spatial motion, and thus Dynkin's proof of existence, which requires multiplicity of the log-Laplace functional, no longer applies. Skoulakis and Adler's method of calculating moments is extended to higher moments, from which existence follows.