Smoothness of self-intersection local time of multidimensional fractional Brownian motion

Xianye Yu

Communications in Statistics - Theory and Methods, 2019, vol. 48, issue 17, 4278-4293

Abstract: In this paper, we study the existence, Hölder continuity and fractional smoothness of the self-intersection local time with respect to fractional Brownian motion:βt(x):=∫0t∫0sδ(BsH−BrH−x)drds, x∈Rd, t∈[0,1]where BH is a d-dimensional fractional Brownian motion with Hurst index H∈(0,1). We also consider the case of intersection local time for two independent multidimensional fractional Brownian motions.

Date: 2019
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DOI: 10.1080/03610926.2018.1493508

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