A Note on Approximating Mean Occupation Times of Continuous-Time Markov Chains
Sheldon M. Ross · Probability in the Engineering and Informational Sciences · 1988
In [1] an approach to approximate the transition probabilities and mean occupation times of a continuous-time Markov chain is presented. For the chain under consideration, let Pij(t) and Tij(t) denote respectively the probability that it is in state j at time t, and the total time spent in j by time t, in both cases conditional on the chain starting in state i. Also, let Y1,…, Yn be independent exponential random variables each with rate λ = n/t, which are also independent of the Markov chain.