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

doi:10.1007/s11464-015-0487-6

Front. Math. China

2015, Vol. 10

Issue (4) : 777-805 https://doi.org/10.1007/s11464-015-0487-6

RESEARCH ARTICLE

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

Zhenlong CHEN¹,Dongsheng WU²,Yimin XIAO^3,^*(

)

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

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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.

Keywords Anisotropic Gaussian field local time collision local time intersection local time self-intersection local time chaos expansion

Corresponding Author(s): Yimin XIAO

Issue Date: 05 June 2015

Cite this article:

Zhenlong CHEN,Dongsheng WU,Yimin XIAO. Smoothness of local times and self-intersection local times of Gaussian random fields[J]. Front. Math. China, 2015, 10(4): 777-805.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0487-6
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I4/777

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