Bounded state space truncation and Censored Markov chains

Markov chain modeling often suffers from the curse of dimensionality problems and many approximation schemes have been proposed in the literature that include state-space truncation. Estimating the accuracy of such methods is difficult and the resulting approximations can be far from the exact solution. Censored Markov chains (CMC) allow to represent the conditional behavior of a system within a subset of observed states and provide a theoretical framework to study state-space truncation. However, the transition matrix of a CMC is in general hard to compute. Dayar et al. (2006) proposed DPY algorithm, that computes a stochastic bound for a CMC, using only partial knowledge of the original chain. We prove that DPY is optimal for the information they take into account. We also show how some additional knowledge on the chain can improve stochastic bounds for CMC.