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Corrected diffusion approximations in certain random walk problems

Published online by Cambridge University Press:  01 July 2016

D. Siegmund
D. Siegmund*
Affiliation:
Stanford University
*
∗Postal address: Department of Statistics, Stanford University, Stanford, CA 94305, U.S.A.
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Abstract

Correction terms are obtained for the diffusion approximation to one- and two-barrier ruin problems in finite and infinite time. The corrections involve moments of ladder-height distributions, and a method is given for calculating them numerically. Examples show that the corrected approximations can be much more accurate than the originals.

Keywords

DIFFUSION APPROXIMATIONHEAVY TRAFFICRANDOM WALKGAMBLER'S RUIN
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 4 , December 1979 , pp. 701 - 719
Copyright
Copyright © Applied Probability Trust 1979 

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Footnotes

Research partially supported by National Science Foundation Grant MCS 77-16974 and by ONR Contract N00014-77-C-0306.

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