Electronic Journal of Probability

Embeddable Markov Matrices

E. Davies

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We give an account of some results, both old and new, about any $n\times n$ Markov matrix that is embeddable in a one-parameter Markov semigroup. These include the fact that its eigenvalues must lie in a certain region in the unit ball. We prove that a well-known procedure for approximating a non-embeddable Markov matrix by an embeddable one is optimal in a certain sense.

Article information

Electron. J. Probab. Volume 15 (2010), paper no. 47, 1474-1486.

Accepted: 28 September 2010
First available in Project Euclid: 1 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J22: Computational methods in Markov chains [See also 65C40] 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 65C40: Computational Markov chains

Markov matrix embeddability Markov generator eigenvalues

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Davies, E. Embeddable Markov Matrices. Electron. J. Probab. 15 (2010), paper no. 47, 1474--1486. doi:10.1214/EJP.v15-733. https://projecteuclid.org/euclid.ejp/1464819832

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