Variance Reduction Techniques for the Simulation of Markov Processes. II. Matrix Iterative Methods.

摘要

Let (x sub n, n > or = 0) be an irreducible, aperiodic, Markov chain with finite state space E, transition matrix P, and stationary distribution pi. Let f be a real valued function on E and define r = pi f. A method of reducing the variance of simulation estimates for r is presented. The method combines the techniques of numerical analysis and simulation by partially solving an appropriate system of linear equations using some matrix iterative procedure and then estimating the difference between the true and partial solutions via simulation. After k iterations of the iterative procedure, functions f sub nu, nu = 0, ..., k are defined so that r = pi f sub nu for each nu.