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On the differential equations for the transition probabilities of Markov processes with enumerably many states

Published online by Cambridge University Press:  24 October 2008

G. E. H. Reuter ,
W. Ledermann  and
M. S. Bartlett
G. E. H. Reuter
Affiliation:
The UniversityManchester
W. Ledermann
Affiliation:
The UniversityManchester
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Extract

Let pik (s, t) (i, k = 1, 2, …; s ≤ t) be the transition probabilities of a Markov process in a system with an enumerable set of states. The states are labelled by positive integers, and pik (s, t) is the conditional probability that the system be in state k at time t, given that it was in state i at an earlier time s. If certain regularity conditions are imposed on the pik, they can be shown to satisfy the well-known Kolmogorov equations§

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 2 , April 1953 , pp. 247 - 262
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

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