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Filtering of a diffusion process with poisson-type observation

  • E. Pardoux
Part II: Research Reports
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 16)

Abstract

We consider a filtering problem, where the signal Xt is a Markov diffusion process, and the observation is a marked point process (for instance a Poisson process), whose predictable projection (the stochastic intensity in the case of a point process) is a given function of the signal Xt.

We associate to this problem a backward stochastic PDE, whose solution is expressible in terms of the conditional law in the filtering problem. It then follows that the forward equation, adjoint to the backward one, governs the evolution of the "unnormalized conditional density".

Analogous results have been proved in the case of an observation corrupted by a Wiener noise in [5] and [6]. The proofs here are more direct.

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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • E. Pardoux
    • 1
  1. 1.(C.N.R.S.) IRIA-LABORIALe ChesnayFrance

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