Hostname: page-component-7bb8b95d7b-495rp Total loading time: 0 Render date: 2024-09-21T06:36:22.370Z Has data issue: false hasContentIssue false
  • English
  • Français

An absorption probability for the Ornstein-Uhlenbeck process

Published online by Cambridge University Press:  14 July 2016

John P. Dirkse
John P. Dirkse*
Affiliation:
George Washington University
Get access Rights & Permissions [Opens in a new window]

Abstract

An asymptotic expression for an absorption probability for the Ornstein-Uhlenbeck process is presented along with an application of the result to a problem in optional stopping. The relation of this result to the asymptotic behavior of a weighted Kolmogorov-Smirnov statistic is also discussed. Sweet and Hardin (1970) derive an exact solution (not in closed form) for this same problem.

Keywords

ASYMPTOTICORNSTEIN-UHLENBECK PROCESSOPTIONAL STOPPINGKOLMOGOROV-SMIRNOV STATISTICLAPLACE TRANSFORM
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 595 - 599
Copyright
Copyright © Applied Probability Trust 1975 

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

Abramowitz, M. and Stegun, I. (1964) Handbook of Mathematical Functions. National Bureau of Standards, Washington, D.C.Google Scholar
Anderson, T. W. and Darling, D. A. (1952) Asymptotic theory of certain goodness of fit criteria based on stochastic processes. Ann. Math. Statist. 23, 193–212,Google Scholar
Bellman, R. and Harris, T. (1951) Recurrence times for the Ehrenfest model. Pacific J. Math. 1, 179–193.CrossRefGoogle Scholar
Brown, B. F. and Mccullum, P. A. (1965) Laplace Transform Tables and Theorems. Holt, Rinehart and Winston, New York, 73.Google Scholar
Darling, D. A. and Siegert, A. J. F. (1953) The first passage problem for a continuous Markov process. Ann. Math. Statist. 24, 624–639.CrossRefGoogle Scholar
Robbins, H. E. (1952) Some aspects of the sequential design of experiments. Bull. Amer. Math. Soc. 58, 527–535.Google Scholar
Rubin, H. (1970) On large sample properties of certain new parametric procedures. Proc. Sixth Berkeley Symp. Math. Statist. Prob. I, 429–435.Google Scholar
Savant, C. J. (1962) Fundamentals of the Laplace Transform. McGraw-Hill, Inc., New York, 127–128.Google Scholar
Sweet, A. L. and Hardin, J. C. (1970) Solutions for diffusion processes with two barriers. J. Appl. Prob. 7, 423–431.Google Scholar