Statistics Seminar: Dongsheng Wu (University of Alabama) -- Regularity of Local Times of Fractional Brownian Sheets

Abstract:

As typical anisotropic Gaussian random fields, fractional Brownian sheets 
have been intensively studied in recent years. In this talk, we study the 
regularity of local times of fractional Brownian sheets, including the 
existence, joint continuity and smoothness (in the Meyer-Watanabe sense) 
of the local times. As applications, we derive regularity results of their 
collision local times, intersection local times and self-intersection 
local times. The main tools applied in our derivation are sectorial local 
nondeterminism of fractional Brownian sheets, Fourier analysis and chaos 
expansion of the local times. 

This talk is based on joint works with A. Ayache, Z. Chen and Y. Xiao.