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.
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Chen, Z., Wu, D. & Xiao, Y. Smoothness of local times and self-intersection local times of Gaussian random fields. Front. Math. China 10, 777–805 (2015). https://doi.org/10.1007/s11464-015-0487-6
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DOI: https://doi.org/10.1007/s11464-015-0487-6
Keywords
- Anisotropic Gaussian field
- local time
- collision local time
- intersection local time
- self-intersection local time
- chaos expansion