Extremes of multifractional Brownian motion

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