一类鞅差序列加权和的Baum-Katz大数定律的精确渐近性

Precise Asymptotics in the Baum-Kate Law of Large Numbers for a Kind of Weighted Sum of Martingale Difference

设ξi,i,1≤i<∞为适应的鞅差序列,cnk:1≤k≤n为双下标常数列,文章获得了一类鞅差序列加权和Sn=∑nk=1cnkξk的Baum-Katz大数定律的精确渐近,给出了∑n≥1nrp-2P|Sn|≥εn1p,∑n≥11P|S|≥εn1p当ε→0时的精确渐近性.

Let {ξi,Zi,1≤i〈∞} be a adaptable martingale difference, {cnk：1≤k≤n} be a constant sequence with double subscript, the paper has obtained precise asymptotics in the Baum-Katz law of large numbers for a kind of weighted sum of martingale difference, and given the precise asymptotics for ∑ni≥1 n^r/p-2P（｜Sn｜≥εn1/p）,∑ni≥1,1/nP（｜Sn｜≥εn1/p） as ε→0.