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Comment on ‘Corrected diffusion approximations in certain random walk problems'

Published online by Cambridge University Press:  14 July 2016

Michael L. Hogan
Michael L. Hogan*
Affiliation:
Columbia University
*
∗Postal address: Department of Statistics, Columbia University, New York, NY 10027, USA.
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Abstract

Correction terms for the diffusion approximation to the maximum and ruin probabilities for a random walk with small negative drift, obtained by Siegmund (1979) in the exponential family case, are extended by different methods to some non-exponential family cases.

Keywords

HEAVY TRAFFICGAMBLER'S RUIN
Type
Research Papers
Information
Journal of Applied Probability , Volume 23 , Issue 1 , March 1986 , pp. 89 - 96
Copyright
Copyright © Applied Probability Trust 1986 

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References

Breiman, L. (1968) Probability. Addison-Wesley, Reading, Ma.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and its Applications. Wiley, New York.Google Scholar
Hochstadt, H. (1973) Integral Equations. Wiley, New York.Google Scholar
Hogan, M. H. (1984) Some Problems in Boundary Crossing for Random Walks. Ph.D. Dissertation, Department of Statistics, Stanford University.Google Scholar
Kingman, J. F. C. (1962) Some inequalities for the queue GI/G/I. Biometrika 49, 315–324.Google Scholar
Klass, M. (1983) On the maximum of a random walk with small negative drift. Ann. Prob. 11, 491–505.Google Scholar
Siegmund, D. (1979) Corrected diffusion approximations in certain random walk problems. Adv. Appl. Prob. 11, 701–719.Google Scholar
Spitzer, F. (1957) The Wiener-Hopf equation whose kernel is a probability density. Duke J. Math. 27, 363–372.Google Scholar
Stein, E. M. (1970) Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, NJ.Google Scholar
Woodroofe, M. (1982) Nonlinear Renewal Theory in Sequential Analysis. SIAM Publications, Philadelphia, Pa.Google Scholar