A consistent algorithm for derivative estimation of Markov chains

A consistent algorithm for derivative estimation of finite-state, discrete-time Markov chains is presented. The basic idea is to simulate original Markov chains with modified performance measures that can be estimated by extra simulation. The computational load of the extra simulation at each step is bounded. The algorithm attains the best possible rate of convergence as the simulation time goes to infinity. A connection between the algorithm and solutions to Poisson equations is also revealed.<<ETX>>