Exact simulation vs exact estimation

Abstract

This paper contrasts exact simulation against exact estimation in two different computational settings, namely that of numerical solution of stochastic differential equations and also in the context of equilibrium calculations for Markov chains. Both exact simulation and exact estimation methods can provide unbiased estimators capable of converging at square root rate in the computational effort c in problems in which conventional methods lead to sub-square root rates. We argue that the relaxation from exact simulation to exact estimation is often useful, because exact estimation algorithms can be easier to design and they can apply in settings in which exact simulation methods are currently unavailable.