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Identities for passage times with applications to recurrent events and homogeneous differential functions

Published online by Cambridge University Press:  14 July 2016

John N. Darroch
John N. Darroch*
Affiliation:
University of Michigan
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Let x be a non-negative, non-decreasing, right-continuous function of t defined on the interval [O, T) and let A = x(T–). Define the function y on [O, A] by Then y is non-decreasing and left-continuous and If t is a time variable it is natural to call y the passage time function.

Type
Research Papers
Information
Journal of Applied Probability , Volume 3 , Issue 2 , December 1966 , pp. 435 - 444
Copyright
Copyright © Applied Probability Trust 

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References

Cox, D. R. (1962) Renewal Theory. Methuen, London.Google Scholar
Darroch, J. N. and Morris, K. W. (1965) Passage-times in Finite Markov Chains. In preparation.Google Scholar
David, F. N. and Barton, D. E. (1962) Combinatorial Chance. Griffin, London.CrossRefGoogle Scholar
Feller, W. (1957) An Introduction to Probability Theory and its Applications, 2nd. Ed. John Wiley, New York.Google Scholar