On distribution tail of the maximum of a random walk

[摘要] Let S-n, n greater than or equal to 1, be the partial sums of i.i.d. random variables with negative mean value. Many papers (see, for example, [1, 2, 5, 6, 7, 9, 11]) give us different theorems on the tail behavior of the distribution of sup {S-n, n greater than or equal to 1}. In this paper the final versions of these theorems (with necessary and sufficient conditions) are presented. The main attention is paid to the necessity part of these theorems. (C) 1997 Elsevier Science B.V.

[发布日期] 1997-12-01

[关键词] maximum of a random walk;large deviations;subexponential distribution;Cramer's estimate