Smoothness of Local Times and Self-Intersection Local Times of Gaussian Random Fields

Zhenlong Chen, Dongsheng Wu, Yimin Xiao

Published 2015-04-18Version 1

This paper is concerned with the smoothness (in the sense of Meyer-Watanabe) of the local times of Gaussian random fields. Sufficient and necessary conditions for the existence and smoothness of the local times, collision local times, and self-intersection local times are established for a large class of Gaussian random fields, including fractional Brownian motions, fractional Brownian sheets and solutions of stochastic heat equations driven by space-time Gaussian noise.