Conditioning properties of the stationary distribution for a Markov chain

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Stephen J. Kirkland


Let T be an irreducible stochastic matrix with stationary vector πT . The conditioning of πT under perturbation of T is discussed by providing an attainable upper bound on the absolute value of the derivative of each entry in πT with respect to a given perturbation matrix. Connections are made with an existing condition number for πT , and the results are applied to the class of Markov chains arising from a random walk on a tree.

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