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On semi-Markov processes on arbitrary spaces

Published online by Cambridge University Press:  24 October 2008

Erhan Çinlar
Affiliation:
Northwestern University, Evanston, Illinois

Extract

Let E be an arbitrary set, a σ-algebra of subsets of

the Borel sets of F. We write A × B for the product of the sets A and B, and

for the product σ-algebra of and (i.e. the σ-algebra generated by the rectangles A × B with A and B).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Çinlar, E.Markov renewal theory. To appear in Adv. Appl. Prob. 1 (1969).CrossRefGoogle Scholar
(2)Dynkin, E. B.Markov processes, 1 (Springer-Verlag; Berlin, 1965).Google Scholar
(3)Feller, W.Boundaries induced by non-negative matrices. Trans. Amer. Math. Soc. 79 (1956), 541–55.Google Scholar
(4)Feller, W.On semi-Markov processes. Proc. Nat. Acad. Sci. U.S.A. 51 (1964), 653659.Google Scholar
(5)Feller, W.An introduction to probability theory and its applications, 2 (Wiley; New York, 1966).Google Scholar
(6)Ito, Y.Invariant measures for Markov processes. Trans. Amer. Math. Soc. 110 (1964), 152184.CrossRefGoogle Scholar
(7)Lévy, P.Processus semi-markoviens Proc. Int. Congr. Math. (Amsterdam) 3 (1954), 416426.Google Scholar
(8)Neveu, J.Sur l'existence des mesures invariantes en théorie ergodique. C. R. Acad. Sci. Paris, Sér. A–B 260 (1965), 393396.Google Scholar
(9)Pyke, R.Markov renewal processes: definitions and preliminary properties. Ann. Math. Statist. 32 (1961), 12311242.CrossRefGoogle Scholar
(10)Pyke, R. and Schaufele, R. A.Limit theorems for Markov renewal processes. Ann. Math. Statist. 35 (1964), 17461764.Google Scholar
(11)Smith, W. L.Regenerative stochastic processes. Proc. Roy. Soc. (London), Ser. A 232 (1955), 631.Google Scholar