This article is cited in 5 papers

Short Communications

A small deviation theorem for independent random variables

Q. M. Shao

Department of Mathematics, Hangzhou University, Hangzhou, P. R. China

Abstract: Let $\{X_n,\,n\ge 1\}$ be a sequence of independent, not necessarily identically distributed random variables. Put $S_k(n)=\sum_{i=1+k}^{n+k}X_i$. A small deviation theorem, i.e., the asymptotic bound of $\mathbf P(\max_{i\le n}|S_k (i)|\le x_{k,n})$ is obtained under a uniform Lindeberg's condition.

Keywords: small deviation, partial sums, independent random variables.

Received: 25.06.1991

Language: English

 English version: Theory of Probability and its Applications, 1995, 40:1, 191–200

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