Let {X, X<sub>n</sub>;n≥1} be a sequence of i.i.d.r.v.s with EX=0 and EX<sup>2</sup>=σ<sup>2</sup>（0【σ【∞）. S<sub>n</sub>=sum from i=1 to n X<sub>l</sub&...Let {X, X<sub>n</sub>;n≥1} be a sequence of i.i.d.r.v.s with EX=0 and EX<sup>2</sup>=σ<sup>2</sup>（0【σ【∞）. S<sub>n</sub>=sum from i=1 to n X<sub>l</sub> We obtain some sufficient and necessary conditions for lim sup max max |S<sub>N</sub>-S<sub>N-j</sub>|/{2σ<sup>2</sup>k（log N/k+log logk）}<sup>1/2</sup>=1 a,s to hold, get the widest range of k’s and answer a question of Hanson and Russo（1983）.展开更多
基金National Natural Science Foundation of China and China Postdoctoral Science Foundation
文摘Let {X, X<sub>n</sub>;n≥1} be a sequence of i.i.d.r.v.s with EX=0 and EX<sup>2</sup>=σ<sup>2</sup>（0【σ【∞）. S<sub>n</sub>=sum from i=1 to n X<sub>l</sub> We obtain some sufficient and necessary conditions for lim sup max max |S<sub>N</sub>-S<sub>N-j</sub>|/{2σ<sup>2</sup>k（log N/k+log logk）}<sup>1/2</sup>=1 a,s to hold, get the widest range of k’s and answer a question of Hanson and Russo（1983）.
