CONVERGENCE-RATES OF FINITE-DIFFERENCE SENSITIVITY ESTIMATES FOR STOCHASTIC-SYSTEMS

A mean square error analysis of finite-difference sensitivity estimato rs for stochastic systems is presented and an expression for the optim al size of the increment is derived. The asymptotic behavior of the op timal increments, and the behavior of the corresponding optimal finite -difference (FD) estimators are investigated for finite-horizon experi ments. Steady-state estimation is also considered for regenerative sys tems and in this context a convergence analysis of ratio estimators is presented. The use of variance reduction techniques for these FD esti mates, such as common random numbers in simulation experiments, is not considered here, In the case here, direct gradient estimation techniq ues (such as perturbation analysis and likelihood ratio methods) whene ver applicable, are shown to converge asymptotically faster than the o ptimal FD estimators.