数学物理学报(英文版) ›› 1997, Vol. 17 ›› Issue (2): 190-197.
张立新
Zhang Lixin
摘要: Let {X(t), t > 0} be a fractional Brownian motion of order 2α with 0 < α <1,β > 0 be a real number, aT be a function of T and 0 < aT ≤ T, limT→∞(log T/aT)/log log T=r, (0 ≤ r ≤ ∞). In this paper, we proved that
c1((r)/1+r)α ≤ lim infT→∞(log log T)β maxaT ≤ t ≤ T(|X(T)+X(T-t)|)/tα(log(T/t)+log logt)β ≤ c2((r)/1+r)α,a.s. where c1, c2 are two positive constants depending only on α,β.