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A central limit theorem for processes defined on a finite Markov chain

Published online by Cambridge University Press:  24 October 2008

J. Keilson  and
D. M. G. Wishart
J. Keilson
Affiliation:
University of Birmingham
D. M. G. Wishart
Affiliation:
University of Birmingham
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Extract

We shall be concerned in this paper with a class of temporally homogeneous Markov processes, {R(t), X(t)}, in discrete or continuous time taking values in the space

The marginal process {X(t)} in discrete time is, in the terminology of Miller (10), a sequence of random variables defined on a finite Markov chain. Probability measures associated with these processes are vectors of the form

where

We shall call a vector of the form of (0·2) a vector distribution.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 3 , July 1964 , pp. 547 - 567
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

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