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Some mean first-passage time approximations for the Ornstein-Uhlenbeck process

Published online by Cambridge University Press:  14 July 2016

Marlin U. Thomas
Marlin U. Thomas*
Affiliation:
Naval Postgraduate School, Monterey, California
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Abstract

This paper describes an accurate method of approximating the mean of the first-passage time distribution for an Ornstein-Uhlenbeck process with a single absorbing barrier. The accuracy of the approximation is demonstrated through some numerical comparisons.

Keywords

ORNSTEIN-UHLENBECK PROCESSDIFFUSION APPROXIMATIONSFIRST-PASSAGE TIMES
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 600 - 604
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Abramowitz, M. and Stegun, I. A. (1964) Handbook of Mathematical Functions. National Bureau of Standards, Washington, D.C.Google Scholar
[2] Cox, D. R. and Miller, H. D. (1965) The Theory of Stochastic Processes. Methuen, London.Google Scholar
[3] Darling, D. and Siegert, A. J. F. (1953) The first passage problem for a continuous Markov process. Ann. Math. Statist. 24, 624–639.CrossRefGoogle Scholar
[4] Hoyt, J. P. (1968) A simple approximation to the standard normal probability density function. Amer. Statistician 22, 25–26.Google Scholar
[5] Iglehart, D. L. (1965) Limiting diffusion approximations for the many server queue and the repairman problem. J. Appl. Prob. 2, 429–441.CrossRefGoogle Scholar
[6] Johnson, N. L. and Kotz, S. (1970) Continuous Univariate Distributions—1 . Houghton Mifflin Company, Boston.Google Scholar
[7] Keilson, J. and Ross, H. (1971) Passage time distributions for the Ornstein-Uhlenbeck process: Preliminary Report. Center for System Science, Tech. Rep. CSS 71–08, University of Rochester (forthcoming IMS Tables).Google Scholar
[8] Mcneil, D. R. and Schach, S. (1973) Central limit analogues for Markov population processes. J. R. Statist. Soc. B 35, 1–23.Google Scholar