Smoothness of higher order derivative of self-intersection local time for fractional Brownian motion

Qian Yu, Qiangqiang Chang and Guangjun Shen

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 10, 3541-3556

Abstract: In a recent paper, Yu (2021) define a k=(k1,k2,…,kd)-th order derivative of self-intersection local times with respect to d-dimensional fractional Brownian motion. By the existence and Hölder continuity proved in Yu (2021), we study the smoothness of derivative of self-intersection local times with respect to fractional Brownian motion in this paper. We also consider the cases of intersection local times and collision local times, respectively.

Date: 2023
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DOI: 10.1080/03610926.2021.1977322

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