Superefficient Simulation of Markov Chains and Semi-Markov Processes.

Abstract : This paper describes a method of simulating a Markov chain for the purpose of estimating functions of the chain and functions of associated semi-Markov processes. In particular, special attention is devoted to the estimation of the probability density function of first passage time from, say, state a to state b. Rotation sampling is used to achieve variances of estimators of order 0(1/k squared), where k is the number of replications, which compares with 0(1/k) when independently sampled replications are used. Since both independent and rotation sampling have computation time complexity 0(k), the relative advantage of rotation sampling is clear as k implies infinity. The paper presents two examples to illustrate the method. (Author)