 

Philippe Carette
Characterizations of Embeddable 3×3 Stochastic Matrices with a Negative Eigenvalue


Published: 
June 20, 1995 
Keywords: 
Continuoustime Markov chain, stochastic matrix, matrix exponential, embedding problem 
Subject: 
60J27,15A51 


Abstract
The problem of identifying a stochastic matrix as a transition matrix
between two fixed times, say t=0 and t=1, of a continuoustime and
finitestate Markov chain has been shown to have practical importance,
especially in the area of stochastic models applied to social
phenomena. The embedding problem of finite Markov chains, as it is
called, comes down to investigating whether the stochastic matrix can
be expressed as the exponential of some matrix with row sums equal to
zero and nonnegative offdiagonal elements. The aim of this paper is
to answer a question left open by S. Johansen (1974), i.e., to
characterize those stochastic matrices of order three with an
eigenvalue λ < 0 of multiplicity 2.


Author information
Centrum voor Statistiek en Operationeel Onderzoek, Vrije Universiteit Brussel, Belgium
phcarett@vub.ac.be

