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A finite dimensional abstract approximation and convergence theory isdeveloped for estimation of the distribution of random parameters in infinitedimensional discrete time linear systems with dynamics described by regularlydissipative operators and involving, in general, unbounded input and outputoperators. By taking expectations, the system is re-cast as an equivalentabstract parabolic system in a Gelfand triple of Bochner spaces wherein therandom parameters become new space-like variables. Estimating theirdistribution is now analogous to estimating a spatially varying coefficient ina standard deterministic parabolic system. The estimation problems areapproximated by a sequence of finite dimensional problems. Convergence isestablished using a state space-varying version of the Trotter-Kato semigroupapproximation theorem. Numerical results for a number of examples involving theestimation of exponential families of densities for random parameters in adiffusion equation with boundary input and output are presented and discussed.

Estimation of the Distribution of Random Parameters in Discrete Time  Abstract Parabolic Systems with Unbounded Input and Output: Approximation and  Convergence