期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1992
卷号：15
DOI：10.1155/S0161171292000644
出版社：Hindawi Publishing Corporation
摘要：Let X, Xn, n≥1 be a sequence of iid real random variables, and Sn=∑k=1nXk, n≥1. Convergence rates of moderate deviations are derived, i.e., the rate of convergence to zero of certain tail probabilities of the partial sums are determined. For example, we obtain equivalent conditions for the convergence of series ∑n≥1(ψ2(n)/n)P(|Sn|≥nφ(n)) only under the assumptions convergence that EX=0 and EX2=1, where φ and ψ are taken from a broad class of functions. These results generalize and improve some recent results of Li (1991) and Gafurov (1982) and some previous work of Davis (1968). For b∈[0,1] and ϵ>0, letλϵ,b=∑n≥3((loglogn)b/n)I(|Sn|≥(2
