Comparison of Some Direct Methods for Computing Stationary Distributions of Markov Chains
Copyright policy )Comparison of Some Direct Methods for Computing Stationary Distributions of Markov Chains
The purpose of this paper is to report on a comparison of an implementation of a simple direct LU factorization method, suggested by \textit{R. E. Funderlic} and \textit{J. B. Mankin} [ibid. 2, 375-383 (1981; Zbl 0468.65042)], with other direct methods recommended by \textit{C. C. Paige} and \textit{G. P. H. Styan} and \textit{P. G. Wachter} [J. Statist. Comput. Simul. 4, 173-186 (1975; Zbl 0331.60040)], for computing stationary distributions of Markov chains. A backward error analysis is developed and conditioning problems are addressed. The method is stable without pivoting, it is numerical efficient and it lends itself to symmetric pivoting to preserve sparsity.
sparsity schemes, probability distribution vector, Markov chain, Probabilistic methods, stochastic differential equations, Direct numerical methods for linear systems and matrix inversion, stochastic process, Markov chains (discrete-time Markov processes on discrete state spaces), direct methods, stationary distributions, comparison, LU factorization, M-matrix, error analysis
sparsity schemes, probability distribution vector, Markov chain, Probabilistic methods, stochastic differential equations, Direct numerical methods for linear systems and matrix inversion, stochastic process, Markov chains (discrete-time Markov processes on discrete state spaces), direct methods, stationary distributions, comparison, LU factorization, M-matrix, error analysis
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