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On extending classical filtering equations

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  • Kouritzin, Michael A.
  • Long, Hongwei

Abstract

In this paper, we give a direct derivation of the Duncan-Mortensen-Zakai filtering equation, without assuming right continuity of the signal, nor its filtration, and without the usual finite energy condition. As a consequence, the Fujisaki-Kallianpur-Kunita equation is also derived. Our results can be applied to filtering problems in which the signal process has [alpha]-stable ([alpha]>1) components, and the sensor function is linear.

Suggested Citation

  • Kouritzin, Michael A. & Long, Hongwei, 2008. "On extending classical filtering equations," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3195-3202, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:18:p:3195-3202
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    Cited by:

    1. 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.

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