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Higher order derivative of self-intersection local time for fractional Brownian motion
Qian Yu · 2020-08-13 · via math.PR updates on arXiv.org

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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