The method of exchangeable pairs has emerged as an important tool in proving limit theorems for Poisson, normal and other classical approximations. Here the method is used in a simulation context. We estimate transition probabilitites from the simulations and use these to reduce variances. Exchangeable pairs are used as control variates.
Finally, a general approximation theorem is developed that can be complemented by simulations to provide actual estimates of approximation errors.
Digital Object Identifier: 10.1214/lnms/1196283797