A Characterization of Reversible Markov Chains by a Rotational Representation

Let P = (pij), i, j = 1,2,..., n be the matrix of a recurrent Markov chain with stationary vector$\nu > 0$and let R = (rij), i, j = 1,2,..., n be a matrix, where rij= vip ij. If R is a symmetric matrix, we improve Alpern's rotational representation of P. By this representation we characteriz...

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Bibliographic Details
Published in:	The Annals of probability Vol. 19; no. 2; pp. 605 - 608
Main Authors:	del Tio, P. Rodriguez, M. C. Valsero Blanco
Format:	Journal Article
Language:	English
Published:	Hayward, CA Institute of Mathematical Statistics 01-04-1991 The Institute of Mathematical Statistics
Subjects:	15A51 60J10 Exact sciences and technology Markov chains Markov processes Mathematics Matrices measure-preserving transformations Probability and statistics Probability theory and stochastic processes Recurrent Markov chains reversible Markov chains Rotation Sciences and techniques of general use Vertices Markov chain Recurrence Reversibility Symmetric matrix
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Summary:	Let P = (pij), i, j = 1,2,..., n be the matrix of a recurrent Markov chain with stationary vector$\nu > 0$and let R = (rij), i, j = 1,2,..., n be a matrix, where rij= vip ij. If R is a symmetric matrix, we improve Alpern's rotational representation of P. By this representation we characterize the reversible Markov chains.
ISSN:	0091-1798 2168-894X
DOI:	10.1214/aop/1176990443