A Characterization of Reversible Markov Chains by a Rotational Representation
del Tio, P. Rodriguez ; Blanco, M. C. Valsero
Ann. Probab., Tome 19 (1991) no. 4, p. 605-608 / Harvested from Project Euclid
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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.
Publié le : 1991-04-14
Classification:  Recurrent Markov chains,  reversible Markov chains,  measure-preserving transformations,  60J10,  15A51 
@article{1176990443,
     author = {del Tio, P. Rodriguez and Blanco, M. C. Valsero},
     title = {A Characterization of Reversible Markov Chains by a Rotational Representation},
     journal = {Ann. Probab.},
     volume = {19},
     number = {4},
     year = {1991},
     pages = { 605-608},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176990443}
}

del Tio, P. Rodriguez; Blanco, M. C. Valsero. A Characterization of Reversible Markov Chains by a Rotational Representation. Ann. Probab., Tome 19 (1991) no. 4, pp.  605-608. http://gdmltest.u-ga.fr/item/1176990443/