The problem of identifying a stochastic matrix as a transition matrixbetween two fixed times, say t=0 and t=1, of a continuous-time andfinite-state Markov chain has been shown to have practical importance,especially in the area of stochastic models applied to socialphenomena. The embedding problem of finite Markov chains, as it iscalled, comes down to investigating whether the stochastic matrix canbe expressed as the exponential of some matrix with row sums equal tozero and nonnegative off-diagonal elements. The aim of this paper isto answer a question left open by S. Johansen (1974), i.e., tocharacterize those stochastic matrices of order three with aneigenvalue λ 0 of multiplicity 2.
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