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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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References

Conolly, B. W. (1971) On randomized random walks. SIAM Rev. 13 (To appear).Google Scholar
Cox, D. R. (1962) Renewal Theory. Wiley, New York.Google Scholar
Erdélyi, A., et al. (1954) Tables of Integral Transforms. Vol. I. McGraw-Hill, New York.Google Scholar
Feller, W. (1966) An Introduction to Probability Theory and its Applications. Wiley, New York.Google Scholar
Goldstein, S. (1953) On the mathematica of exchange processes in fixed columns. Proc. Roy. Soc. A 219, 151–171.Google Scholar
Good, I. J. (1961) The frequency count of a Markov chain and the transition to continuous time. Ann. Math. Statist. 32, 41–48.Google Scholar
Greenberg, I. (1964) The distribution of busy time for a simple queue. Operat. Res. 12, 503–504.Google Scholar
Linhart, P. B. (1967) Alternating renewal processes with application to some single-server problems. Paper read at the Fifth International Telegraphic Congress, Rockefeller University, New York, June 14–20.Google Scholar
Saaty, T. L. (1961) Elements of Queueing Theory. McGraw-Hill, New York.Google Scholar
Takács, L. (1957) On certain sojourn time problems in the theory of stochastic processes. Acta Math. Acad. Sci. Hung. 8, 169–191.Google Scholar