Generalized self-intersection local time for a superprocess over a stochastic flow

Abstract

This paper examines the existence of the self-intersection local time for a superprocess over a stochastic flow in dimensions $d\le 3$, 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.

Published in at http://dx.doi.org/10.1214/11-AOP653 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)