Embedded population systems in Markov set-chains (Q855539)

A finite Markov chain with \(n\)-states contains a population system if its probability transition matrices \(P(t)=(p_{ij}(t))\), \(t=1,2,3,\dots\), satisfy \(p_{ij}=k_{ij}(t)/\omega_i(t)\), \(1\leq i, j\leq n\), for some positive integers \(\omega_i(t)\) with \(\sum_i\omega_i(t)\) a constant (independent of \(t\)) and non-negative integers \(k_{ij}(t)\). The author shows some (sufficient) bound conditions for the transition matrices under which a Markov set-chain or a matrix set-chain contains a population system.