摘要
Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q（n）be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q（n）≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t≤1B（t）-inf0≤t≤sB（t）,and B（t） is a Brownian bridge.
Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q（n）be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q（n）≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t≤1B（t）-inf0≤t≤sB（t）,and B（t） is a Brownian bridge.
基金
Supported by the NNSF of China(10071072).
