Nonlinear filtering of semi-Dirichlet processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Hu, Ze-Chun²  Ma, Zhi-Ming³  Sun, Wei¹ 

[1] Concordia Univ, Dept Math & Stat, Montreal, PQ H3G 1M8, Canada

[2] Nanjing Univ, Dept Math, Nanjing, Peoples R China

[3] Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100864, Peoples R China

关键词: Nonlinear filtering;    Semi-Dirichlet forms;    Filtering equations;    Uniqueness of solutions;    Wiener chaos expansions;    Density equations;   

DOI  :  10.1016/j.spa.2009.09.006

来源: Elsevier

【 摘 要 】

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. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free