Uniform, in-probability approximation of stochastic systems

A system approximation theory useful for modeling stochastic systems is described. The theory applies to a 'large' class of continuous-time stochastic nonlinear systems characterized by a property called approximate finite memory in probability. Approximation is with respect to the input-output behavior of the system under consideration. 'Tractable' structures are proposed for system approximants along with approximation criteria and general conditions under which these structures satisfy the approximation criteria are given. The fundamental role played by these and related results in system modeling is discussed. Detailed developments of these results are provided by Perryman (see Ph.D dissertation, University of California, 1996).