RESEARCH ARTICLE

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

  • Zhenlong CHEN 1 ,
  • Dongsheng WU 2 ,
  • Yimin XIAO , 3
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  • 1. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China
  • 2. Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, USA
  • 3. Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA

Received date: 08 Feb 2015

Accepted date: 13 Apr 2015

Published date: 05 Jun 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

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.

Cite this article

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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