On the Problem of Establishing the Existence of Stationary Distributions for Continuous-Time Markov Chains
1993 ◽
Vol 7
(4)
◽
pp. 529-543
◽
Keyword(s):
We consider the problem of establishing the existence of stationary distributions for continuous-time Markov chains directly from the transition rates Q. Given an invariant probability distribution m for Q, we show that a necessary and sufficient condition for m to be a stationary distribution for the minimal process is that Q be regular. We provide sufficient conditions for the regularity of Q that are simple to verify in practice, thus allowing one to easily identify stationary distributions for a variety of models. To illustrate our results, we shall consider three classes of multidimensional Markov chains, namely, networks of queues with batch movements, semireversible queues, and partially balanced Markov processes.
2002 ◽
Vol 39
(01)
◽
pp. 197-212
◽
2002 ◽
Vol 39
(1)
◽
pp. 197-212
◽
1991 ◽
Vol 23
(02)
◽
pp. 277-292
◽
2000 ◽
Vol 32
(4)
◽
pp. 1064-1076
◽