On a Decomposition for Infinite Transition Matrices
Heyman gives an interesting factorization of I-P,
where P is the transition probability matrix for
an ergodic Markov Chain.
We show that this factorization is valid if and only if the Markov chain
is recurrent. Moreover, we provide a decomposition result which includes
all ergodic, null recurrent as well as the
transient Markov chains as special cases.
Such a decomposition has been shown to be useful in the analysis
of queues.
Keywords: Stochastic and substochastic matrices, Markov chains,
decomposition and factorization.
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