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

Qian Yu

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

Probability 2020-12-22 v2

Authors: Qian Yu

Abstract

We consider the existence and H\"{o}lder 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).

Keywords

fractional brownian motion self-intersection local time higher order derivative hölder continuity limit theorem

Cite

@article{arxiv.2008.05633,
  title  = {Higher order derivative of self-intersection local time for fractional Brownian motion},
  author = {Qian Yu},
  journal= {arXiv preprint arXiv:2008.05633},
  year   = {2020}
}

Comments

21 pages

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