Solutions of some two-sided boundary problems for sums of variables with alternating distributions
- 1 June 1965
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 2 (02) , 377-395
- https://doi.org/10.1017/s002190020010871x
Abstract
In this paper we present a method for obtaining explicit results for some two-sided boundary problems involving sums of independent random variables with alternating distributions. We apply the method to finding the first passage time to either one of two finite barriers, and to some situations arising in queueing and dam theory. The results can be expressed in terms of a finite sum of simple repeated integrals (or sums) of known functions (cf. formulae (3.6)– (3.11)).Keywords
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