Continuous dependence of stochastic control models on the noise distribution

Given a discrete-time stochastic control systemx_t+1=F(x_t,a_t,_t),t=0, 1,.., N (N), where the noise process {_t} is a sequence of i.i.d. random elements with distribution, let^N (x) be the optimal reward function when the initial state isx and the planning horizon isN. We give conditions under whichv^N is a continuous function in for several reward criteria. The applicability of these results to nonparametric adaptive control of stochastic systems is briefly discussed.This research was supported in part by the Consejo Nacional de Ciencia y Tecnologia (CONACYT) under Grants PCCBBNA-020630 and PCEXCNA-040640.