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The calculation of limit probabilities for denumerable Markov processes from infinitesimal properties

Published online by Cambridge University Press:  14 July 2016

Richard L. Tweedie
Richard L. Tweedie*
Affiliation:
University of Cambridge
*
∗ Now at the Australian National University, Canberra.
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Abstract

The problem considered is that of estimating the limit probability distribution (equilibrium distribution) πof a denumerable continuous time Markov process using only the matrix Q of derivatives of transition functions at the origin. We utilise relationships between the limit vector πand invariant measures for the jump-chain of the process (whose transition matrix we write P∗), and apply truncation theorems from Tweedie (1971) to P∗. When Q is regular, we derive algorithms for estimating πfrom truncations of Q; these extend results in Tweedie (1971), Section 4, from q-bounded processes to arbitrary regular processes. Finally, we show that this method can be extended even to non-regular chains of a certain type.

Keywords

DENUMERABLE MARKOV PROCESSLIMIT DISTRIBUTIONEQUILIBRIUM DISTRIBUTIONTRUNCATIONRATE MATRIXJUMP-CHAINFINITE APPROXIMATIONSREGULARITYINVARIANT MEASURESSTATIONARY MEASURES
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 1 , March 1973 , pp. 84 - 99
Copyright
Copyright © Applied Probability Trust 1973 

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