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Delayed random walks

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  • Lemoine, Austin J.

Abstract

A delayed random walk {S*n, n >= 0} is defined here as a partial sum process of independent random variables in which the first N summands (N optional) are distributed F1,...,FN, respectively, while all remaining summands are distributed F0, where {Fk, k >= 0} is a sequence of proper distribution functions on the real line. Delayed random walks arise naturally in the study of certain generalized single server queues. This paper examines optional times of the process such as [pi] = inf {n: n >= 1 and S*n >= 0}. Conditions insuring the finiteness of E {[pi]} and E {[pi]2} are obtained, generating functions calculated, and illustrative examples given. The bivariate functions E{r[pi]explsqbitS*[pi]rsqb} and are studied for the case where N [reverse not equivalent] 1.

Suggested Citation

  • Lemoine, Austin J., 1973. "Delayed random walks," Stochastic Processes and their Applications, Elsevier, vol. 1(3), pages 251-268, July.
    • Handle: RePEc:eee:spapps:v:1:y:1973:i:3:p:251-268
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