On the moments of some first passage times for sums of dependent random variables

Allan Gut

Stochastic Processes and their Applications, 1974, vol. 2, issue 1, 115-126

Abstract: Let Sn,n = 1, 2, ..., denote the partial sums of integrable random variables. No assumptions about independence are made. Conditions for the finiteness of the moments of the first passage times N(c) = min {n: Sn>ca(n)}, where c >= 0 and a(y) is a positive continuous function on [0, [infinity]), such that a(y) = o(y) as y --> [infinity], are given. With the further assumption that a(y) = yP, 0 [infinity] are obtained. The corresponding stopped sums are also studied.

Date: 1974
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