Nonlinear filtering of semi-Dirichlet processes

Ze-Chun Hu, Zhi-Ming Ma and Wei Sun

Stochastic Processes and their Applications, 2009, vol. 119, issue 11, 3890-3913

Abstract: Herein, we consider the nonlinear filtering problem for general right continuous Markov processes, which are assumed to be associated with semi-Dirichlet forms. First, we derive the filtering equations in the semi-Dirichlet form setting. Then, we study the uniqueness of solutions of the filtering equations via the Wiener chaos expansions. Our results on the Wiener chaos expansions for nonlinear filters with possibly unbounded observation functions are novel and have their own interests. Furthermore, we investigate the absolute continuity of the filtering processes with respect to the reference measures and derive the density equations for the filtering processes.

Keywords: Nonlinear; filtering; Semi-Dirichlet; forms; Filtering; equations; Uniqueness; of; solutions; Wiener; chaos; expansions; Density; equations (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (1)

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