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Nonlinear filtering of semi-Dirichlet processes

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

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.

Suggested Citation

  • Hu, Ze-Chun & Ma, Zhi-Ming & Sun, Wei, 2009. "Nonlinear filtering of semi-Dirichlet processes," Stochastic Processes and their Applications, Elsevier, vol. 119(11), pages 3890-3913, November.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:11:p:3890-3913
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    References listed on IDEAS

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    1. Kouritzin, Michael A. & Long, Hongwei, 2008. "On extending classical filtering equations," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3195-3202, December.
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    Cited by:

    1. Matthew J. Lindquist & Joeri Sol & Mirjam Van Praag, 2015. "Why Do Entrepreneurial Parents Have Entrepreneurial Children?," Journal of Labor Economics, University of Chicago Press, vol. 33(2), pages 269-296.

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