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arXiv · 2008.05633

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

Qian Yu
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Abstract

We consider the existence and Hölder continuity conditions for the $k$-th order derivatives of self-intersection local time for $d$-dimensional fractional Brownian motion, where $k=(k_1,k_2,\cdots, k_d)$. Moreover, we show a limit theorem for the critical case with $H=\frac{2}{3}$ and $d=1$, which was conjectured by Jung and Markowsky (2014).

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Qian Yu. 2020-12-21. Higher order derivative of self-intersection local time for fractional Brownian motion. https://arxiv.org/abs/2008.05633

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