Extremes of multifractional Brownian motion

Long Bai

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arXiv · 1711.05725

Extremes of multifractional Brownian motion

Long Bai

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Abstract

Let $B_{H}(t), t\geq [0,T], T\in(0,\infty)$ be the standard Multifractional Brownian Motion(mBm), in this contribution we are concerned with the exact asymptotics of \begin{eqnarray*} \mathbb{P}\left\{\sup_{t\in[0,T]}B_{H}(t)>u\right\} \end{eqnarray*} as $u\rightarrow\infty$. Mainly depended on the structures of $H(t)$, the results under several important cases are investigated.

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Long Bai. 2017-11-15. Extremes of multifractional Brownian motion. https://arxiv.org/abs/1711.05725

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