Uniqueness and robustness of solution of measure-valued equations of nonlinear filtering
After an introduction, in the second part of the paper some necessary preliminary results are presented. The main section of the article is the third one. Here, assuming that the signal process which is a Markov one, takes values in a complete separable metric space, pathwise uniqueness of solution of the Zakai equation under a set of conditions is proved. In Section 4, an important special case of independent signal and noise is presented. The extension to the infinite dimensions is done in Section 5. Applying the results to signals taking values in Hilbert space, in Section 6 this can be done to models of environmental pollution. In Section 7, results are applied to a signal which is modelled by a semilinear stochastic differential equation on a Hilbert space. In the last two parts the statistical robustness is analyzed.
scientific article; zbMATH DE number 897281