LIKELIHOOD RATIO GRADIENT ESTIMATION FOR STOCHASTIC RECURSIONS

In this paper, we develop mathematical machinery for verifying that a broad class of general state space Markov chains reacts smoothly to ce rtain types of perturbations in the underlying transition structure. O ur main result provides conditions under which the stationary probabil ity measure of an ergodic Harris-recurrent Markov chain is differentia ble in a certain strong sense. The approach is based on likelihood rat io 'change-of-measure' arguments, and leads directly to a 'likelihood ratio gradient estimator' that can be computed numerically.