Smoothness of local times and self-intersection local times of Gaussian random fields.

Chen, Zhenlong; Wu, Dongsheng; Xiao, Yimin

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.

GAUSSIAN distribution; ASYMPTOTIC normality; LOCAL times (Stochastic processes); WIENER processes; MARKOV processes

Frontiers of Mathematics in China, 2015, Vol 10, Issue 4, p777

1673-3452

Academic Journal

10.1007/s11464-015-0487-6