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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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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Abstract	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.
AbstractList	Let P = (p_{ij}), i, j = 1,2,\ldots, n be the matrix of a recurrent Markov chain with stationary vector \nu > 0 and let R = (r_{ij}), i, j = 1,2,\ldots, n be a matrix, where r_{ij} = v_ip_{ij}. If R is a symmetric matrix, we improve Alpern's rotational representation of P. By this representation we characterize the reversible Markov chains. 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.
Author	M. C. Valsero Blanco del Tio, P. Rodriguez
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SubjectTerms	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
Title	A Characterization of Reversible Markov Chains by a Rotational Representation
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