Electronic Journal of Probability

Embeddable Markov Matrices

E. Davies

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819832

Digital Object Identifier
doi:10.1214/EJP.v15-733

Mathematical Reviews number (MathSciNet)
MR2727318

Zentralblatt MATH identifier
1226.60102

Subjects
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

Keywords
Markov matrix embeddability Markov generator eigenvalues

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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