On the Computation of Density Functions of Parameters in Stochastic Systems

摘要

A time-discrete stochastic system is defined by means of a probability triplet (an experiment) E = (S, F, P) which determines the density function of the parameter in the system. The effect of a measurement (through a change of the probability measure P in the experiment) in the stochastic system is investigated. It is shown that as a result of the measurement the parameter can be substituted by an a posteriori parameter with dimension one less than the dimension of the parameter. The problems consist of the computation of various conditional density functions assuming that a measurement on a realization of the stochastic system has been made. The solutions are given as algorithms involving only matrix computations of fixed dimensionality. (Author)