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The Ruin Problem for Sums of Dependent Random Variables

Published online by Cambridge University Press:  20 November 2018

Dudley Paul Johnson
Dudley Paul Johnson*
Affiliation:
Department of Mathematics University of Calgary 2920, 24 Avenue N.W. Calgary Alberta T2N IN4
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Abstract

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In this paper we show how to compute the probability that a sequence Zn = X0 + … + Xn of partial sums of dependent random variables, each taking on the values ±1, will first leave an interval (a, b) at a; and how to compute the expected time it takes for the partial sums to leave the interval (a, b).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 3 , 01 September 1980 , pp. 333 - 337
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Dunford, N. and Schwartz, S. (1958). Linear Operators I: General theory. Pure and Appl. Math., Vol. 7, Interscience, New York.Google Scholar