Strong local nondeterminism for FBm

Let $B ^\alpha$ is a $ (n,1) $-fractional Brownian motion with index $\alpha\in (0,1). $ Pitt (Local times for Gaussian vector Fields, Indiana Univ. Math. J. 1978)

proved that $B ^\alpha$ satisfies the following strong local nondeterminism:there exists a constant $0<c_1<\infty$ s Uch that, for all integers $n \ge 1$ and all $u, T^1,\ldots,t^n\in r^n$,

$ $Var (B^\alpha (U) | B^\alpha (t^1), \ldots,b^\alpha (t^n)) \ge c_1 \min_{0\le k\le n}|u-t^k|^{2\alpha},$$

where $t ^0=0.$

Wu and Xiao (dimensional properties of fractional Brownian motion, Act Math Sin,) showed that it's equivalent to the Following:

There Exista a constant $0<c_2<\infty$ such that, for all integers $n \ge 1$ and all $u, V, T^1,\ldots,t^n\in r^n$,

$ $Var (B^\alpha (U)-b^\alpha (v) | B^\alpha (t^1), \ldots,b^\alpha (t^n)) \ge c_2\min (\min_{0\le k\le n}|u-t^k|^{2\alpha}+\min_{0\le k\le n}|v-t^k|^{2\ Alpha}, |u-v|^{2\alpha}). $$

Strong local nondeterminism for FBm