Polynomial Decay in Absorbing Continuous-Time Markov Chains

Let $P(t)$ be the transition function of an absorbing continuous-time Markov chain on a countable state space. We study asymptotic relations of the form $p_{ij}(t)\sim a_{ij} L(t)$, $t\to\infty$, where $L$ is independent of $i$ and $j$. We obtain general conditions under which the coefficient matrix