On the embedding problem for three-state Markov chains.

The present paper investigates the embedding problem for time-homogeneous Markov chains. A discrete-time Markov chain with time unit 1 is embeddable in case there exists a compatible Markov chain regarding time unit 1/m (with m > 1 integer number). An embeddable Markov chain has a transition matrix for which there exists an m-th root that is a probability matrix. The present paper examines the embedding problem for discrete-time Markov chains with three states. Sufficient embedding conditions are presented in case of a diagonalizable transition matrix with all eigenvalues nonnegative.

ISBN:978-988-19253-5-0

Publication year:2014

Keywords:Markov chain, embedding problem