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On three classical problems for Markov chains with continuous time parameters

Published online by Cambridge University Press:  14 July 2016

Mu-Fa Chen
Mu-Fa Chen*
Affiliation:
Beijing Normal University
*
∗Postal address: Department of Mathematics, Beijing Normal University, Beijing 100875, The People's Republic of China.
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Abstract

For a given transition rate, i.e., a Q-matrix Q = (qij) on a countable state space, the uniqueness of the Q-semigroup P(t) = (Pij(t)), the recurrence and the positive recurrence of the corresponding Markov chain are three fundamental and classical problems, treated in many textbooks. As an addition, this paper introduces some practical results motivated from the study of a type of interacting particle systems, reaction diffusion processes. The main results are theorems (1.11), (1.17) and (1.18). Their proofs are quite straightforward.

Keywords

UNIQUENESSRECURRENCEPOSITIVE RECURRENCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 2 , June 1991 , pp. 305 - 320
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

The author was partially supported by the Ying-Tung Fok Education Foundation and the Natural Science Foundation of China.

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