Frontiers of Mathematics in China >
Smoothness of local times and self-intersection local times of Gaussian random fields
Received date: 08 Feb 2015
Accepted date: 13 Apr 2015
Published date: 05 Jun 2015
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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.
Zhenlong CHEN , Dongsheng WU , Yimin XIAO . Smoothness of local times and self-intersection local times of Gaussian random fields[J]. Frontiers of Mathematics in China, 2015 , 10(4) : 777 -805 . DOI: 10.1007/s11464-015-0487-6
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