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A bivariate distribution in regeneration

Published online by Cambridge University Press:  14 July 2016

Kai Lai Chung
Kai Lai Chung*
Affiliation:
Stanford University
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Abstract

The joint distribution of the time since last exit, and the time until next entrance, into a unique boundary point is given in Formula (1) below. The boundary point may be replaced by a regenerative phenomenon.

Keywords

REGENERATIVE PHENOMENONBOUNDARY THEORYLAST EXITFIRST ENTRANCE
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 4 , December 1975 , pp. 837 - 839
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Chung, K. L. (1970) Lectures on Boundary Theory for Markov Chains. Annals of Mathematics Studies No. 65, Princeton University Press.Google Scholar
[2] Getoor, R. K. (1974) Some remarks on a paper of Kingman. Adv. Appl. Prob. 6, 757–767.CrossRefGoogle Scholar
[3] Kingman, J. F. C. (1966) An approach to the study of Markov processes (with discussion). J. R. Statist. Soc. B 28, 417–447.Google Scholar
[4] Kingman, J. F. C. (1973) Homecoming of Markov processes. Adv. Appl. Prob. 5, 66–102.Google Scholar
[5] Pittenger, A. O. (1970) Boundary decomposition of locally-Hunt processes. Adv. Probability 2, 117–159.Google Scholar
[6] Chung, K. L. (1975) Excursions in Brownian motion (To appear.) Google Scholar