A transition matrix P is said to be doubly stochastic if the sum over each column equals

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A transition matrix P is said to be doubly stochastic if the sum over each column equals 1; that is, M i0 pij 1, for all j.

If such a chain is irreducible, aperiodic, and consists of M 1 states, show that j M 1

1, for j 0, 1, . . . , M.

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Introduction To Operations Research

ISBN: 9780072321692

7th Edition

Authors: Frederick S. Hillier, Gerald J. Lieberman

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