On distribution tail of the maximum of a random walk

D. Korshunov

Stochastic Processes and their Applications, 1997, vol. 72, issue 1, 97-103

Abstract: Let Sn, n [greater-or-equal, slanted] 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 {Sn,n [greater-or-equal, slanted] 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.

Keywords: Maximum; of; a; random; walk; Large; deviations; Subexponential; distribution; Cramer's; estimate (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (12)

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