Computing the stationary distribution for infinite Markov chains |
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Authors: | E Seneta |
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Institution: | Department of Mathematical Statistics University of Sydney, N.S.W. 2006, Australia |
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Abstract: | In a situation where the unique stationary distribution vector of an infinite irreducible positive-recurrent stochastic matrix P is not analytically determinable, numerical approximations are needed. This paper partially synthesizes and extends work on finite-vector approximative solutions obtained from nxn northwest corner truncations (n)P of P, from the standpoints of (pointwise convergence) algorithms as n→∞, and the manner of their computer implementation with a view to numerical stability and conditioning. The problem for finite n is connected with that of finding the unique stationary distribution of the finite stochastic matrix (n)P? obtained from (n)P by augmenting a column. |
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