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

摘要

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