Nonlinear filtering of semi-Dirichlet processes |
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| Authors: | Ze-Chun Hu Zhi-Ming Ma Wei Sun |
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| Institution: | aDepartment of Mathematics, Nanjing University, China;bInstitute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China;cDepartment of Mathematics and Statistics, Concordia University, Canada |
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| 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. |
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| Keywords: | Nonlinear filtering Semi-Dirichlet forms Filtering equations Uniqueness of solutions Wiener chaos expansions Density equations |
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