Stationary Probabilities of Markov Chains with Upper Hessenberg
Transition Matrices
In this paper, based on probabilistic arguments,
we obtain an explicit solution of the stationary distribution
for a discrete time Markov chain with an upper
Hessenberg time stationary transition probability matrix.
Our solution then leads to a numerically stable and efficient algorithm
for computing stationary probabilities.
Two other expressions for the stationary distribution are also
derived, which lead to two alternative algorithms.
Numerical analysis of the algorithms is given, which shows
the reliability and efficiency of the algorithms.
Examples of applications are provided, including results of a discrete
time state dependent batch arrive queueing model.
The idea used in this paper can be generalized to deal with
Markov chains with a more general structure.
Keywords: Stationary probabilities; Hessenberg matrices;
Censored Markov chains.
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