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Incomplete discontinuous Markov processes

Published online by Cambridge University Press:  14 July 2016

J. E. Moyal
J. E. Moyal*
Affiliation:
Argonne National Laboratory, Argonne, Illinois
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Summary

The present paper generalizes the results of the author's paper [2] on “Discontinuous Markov processes” to processes that are incompletely specified. These results are then used to develop a step-by-step method of solution for processes involving several kinds of “jumps”, where at the first step one solves for the transition probabilities involving jumps of the first kind, but not of the second, third, etc., at the second step for transition probabilities involving jumps of the first and second, but not the third, fourth, etc. kinds, and so on. Some examples are given.

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 2 , Issue 1 , June 1965 , pp. 69 - 78
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Heathcote, C. R. and Moyal, J. E. (1959) The random walk in continuous time and its application to the theory of queues. Biometrika 46, 400–411.CrossRefGoogle Scholar
[2] Moyal, J. E. (1957) Discontinuous Markoff processes. Acta Math. 98, 221–264.Google Scholar