Extremes of multifractional Brownian motion

Abstract

Let $B_H(t),t\ge [0,T],T\in (0,\infty )$ 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 $u\to \infty$. Mainly depended on the structures of $H(t)$, the results under several important cases are investigated.