Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-15T01:20:48.512Z Has data issue: false hasContentIssue false

General transition probabilities for finite Markov chains

Published online by Cambridge University Press:  24 October 2008

Marcel F. Neuts
Affiliation:
Purdue University, Lafayette, Ind.

Extract

We consider a stationary discrete-time Markov chain with a finite number m of possible states which we designate by 1,…,m. We assume that at time t = 0 the process is in an initial state i with probability (i = 1,…, m) and such that and .

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1964

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)Feller, William. An introduction to probability theory and its applications, vol. I, 2nd ed. (Wiley; New York, 1957).Google Scholar
(2)Gillis, J.A random walk in the plane. Proc. Cambridge Philos. Soc. 56 (1960), 390392CrossRefGoogle Scholar
(3)Kemperman, J. H. B. Asymptotic expansions for the Smirnov test and for the range of cumulative sums. Ann. Math. Stat. 39 (1959), 448462CrossRefGoogle Scholar
(4)Kemperman, J. H. B.The passage problem for a stationary Markov chain (University of Chicago Press, 1961).CrossRefGoogle Scholar
(5)Neuts, Marcel F.Absorption probabilities for a random walk between a reflecting and an absorbing barrier (Euratom Technical Report No. 8: EUR/C-IS/317/62f).Google Scholar
(6)Weesakul, B.The random walk between a reflecting and an absorbing barrier. Ann. Math. Stat. 32 (1961), 765769CrossRefGoogle Scholar