On the characteristic function of a sum ofM-dependent random variables

[摘要] LetS=f1+f2+…+fnbe a sum of1-dependent random variables of zero mean. Letσ2=ES2,L=σ−3∑1≦i≦nE|fi|3. There is a universal constantasuch that fora|t|L<1, we have|Eexp(itSσ−1)|≦(1+a|t|)sup{(a|t|L)−1/4lnL,   exp(−t2/80)}.This bound is a very useful tool in proving Berry-Esseen theorems.

[学科分类] 数学（综合）