Abstract
The scheme of common random numbers (CRN) is a very popular method for variance reduction in simulation. Finite difference (FD) is a conventional technique for derivative estimation. In this paper, we examine the effectiveness of CRN for improving the rates of convergence for FD estimates over infinite horizon for homogeneous discrete-time Markov chains. For direct FD estimates, we give sufficient conditions for the effectiveness of CRN. Based on these conditions, we also suggest several simulation schemes with guaranteed effectiveness. For ratio estimates based on regenerative structures, we prove that the use of CRN is always advantageous.
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