Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T14:13:43.784Z Has data issue: false hasContentIssue false
  • English
  • Français

Solutions of some two-sided boundary problems for sums of variables with alternating distributions

Published online by Cambridge University Press:  14 July 2016

J. Chover  and
G. Yeo
J. Chover
Affiliation:
University of Wisconsin
G. Yeo
Affiliation:
University of Sheffield
Get access Rights & Permissions [Opens in a new window]

Extract

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)).

Type
Research Papers
Information
Journal of Applied Probability , Volume 2 , Issue 2 , December 1965 , pp. 377 - 395
Copyright
Copyright © Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barrer, D. Y. (1957) Queueing with impatient customers and ordered service. Operat. Res. 5, 650–656.CrossRefGoogle Scholar
Baxter, G. (1961) An analytic approach to finite fluctuation problems in probability. J. d'Analyse Math. 9, 31–70.CrossRefGoogle Scholar
Finch, P. D. (1960) Deterministic customer impatience in the queueing system GI/M/1. Biometrika 47, 45–52.CrossRefGoogle Scholar
Gaver, D. P. and Miller, R. G. (1962) Limiting distributions for some storage problems. Studies in Applied Probability and Management Science. Arrow, et al. (ed.). Stanford University Press.Google Scholar
Riesz, F. and Nagy, B. Sz. (1955) Functional Analysis. Ungar.Google Scholar
Spitzer, F. (1956) A combinatorial lemma and its applications to probability theory. Trans. Amer. Math. Soc. 82, 323–339.CrossRefGoogle Scholar
Weesakul, B. and Yeo, G. F. (1963) Some problems in finite dams with an application to insurance risk. Z. Wahrscheinlichkeitstheorie 2, 135–146.CrossRefGoogle Scholar