A characterization of reversible Markov chains by a rotational representation. (English) Zbl 0727.60074

Rodríguez del Tío, P.; Valsero Blanco, M. C.

Ann. Probab. 19, No. 2, 605-608 (1991).

Summary: Let \(P=(p_{ij})\), \(i,j=1,2,...,n\), be the matrix of a recurrent Markov chain with stationary vector \(v>0\) and let \(R=(r_{ij})\), \(i,j=1,2,...,n\), 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.

MSC:

60J10	Markov chains (discrete-time Markov processes on discrete state spaces)
15B51	Stochastic matrices

Keywords:

recurrent Markov chain; rotational representation; reversible Markov chains