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On a three-state sojourn time problem

Published online by Cambridge University Press:  14 July 2016

A. E. Gibson  and
B. W. Conolly
A. E. Gibson
Affiliation:
Bell Telephone Laboratories, Whippany, New Jersey
B. W. Conolly
Affiliation:
SACLANT ASW Research Centre, La Spezia, Italy
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Extract

Consider the real-valued stochastic process {S(t), 0 ≦ t < ∞} which assumes values in an arbitrary space X. For a given subset T ⊂ X we define which represents the length in time of a visit to state T. We shall restrict ourselves to processes such that τT is a random variable having a differentiable distribution function which is independent of the time t0 at which the visit to state T begins.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 4 , December 1971 , pp. 716 - 723
Copyright
Copyright © Applied Probability Trust 1971 

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