Hostname: page-component-7bb8b95d7b-2h6rp Total loading time: 0 Render date: 2024-10-06T19:23:03.346Z Has data issue: false hasContentIssue false
  • English
  • Français

On semi-Markov processes on arbitrary spaces

Published online by Cambridge University Press:  24 October 2008

Erhan Çinlar
Erhan Çinlar
Affiliation:
Northwestern University, Evanston, Illinois
Get access Rights & Permissions [Opens in a new window]

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
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 2 , September 1969 , pp. 381 - 392
Copyright
Copyright © Cambridge Philosophical Society 1969

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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), 653–659.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), 152–184.CrossRefGoogle Scholar
(7)Lévy, P.Processus semi-markoviens Proc. Int. Congr. Math. (Amsterdam) 3 (1954), 416–426.Google Scholar
(8)Neveu, J.Sur l'existence des mesures invariantes en théorie ergodique. C. R. Acad. Sci. Paris, Sér. A–B 260 (1965), 393–396.Google Scholar
(9)Pyke, R.Markov renewal processes: definitions and preliminary properties. Ann. Math. Statist. 32 (1961), 1231–1242.CrossRefGoogle Scholar
(10)Pyke, R. and Schaufele, R. A.Limit theorems for Markov renewal processes. Ann. Math. Statist. 35 (1964), 1746–1764.Google Scholar
(11)Smith, W. L.Regenerative stochastic processes. Proc. Roy. Soc. (London), Ser. A 232 (1955), 6–31.Google Scholar