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A Stroock Varadhan support theorem in non-linear filtering theory
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  • Published: March 1990

A Stroock Varadhan support theorem in non-linear filtering theory

  • M. Chaleyat-Maurel1 &
  • D. Michel2 

Probability Theory and Related Fields volume 84, pages 119–139 (1990)Cite this article

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Summary

Let (ρ t ϕ)0≦t≦1 be the unnormalized filter arising in the filtering theory of correlated diffusions. In this article, ϱ. φ. is considered as a stochastic process taking values inC(ℝn,ℝ); a description of the support of its law in the Fréchet spaceC([0,1],C(ℝn,R)) is given. This result is the analogue for stochastic partial differential equations of the celebrated Stroock-Varadhan theorem for diffusion processes. The support of the law of the filter is shown to be the closure of the set of trajectories obtained from the Zakai equation by replacing the Stratonovitch differentialdy by anH 1-control (herey denotes the observation process).

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Author information

Authors and Affiliations

  1. Laboratoire de Probabilités, Université Paris VI, Tour 56, 4, Place Jussieu, F-75252, Paris Cedex 05, France

    M. Chaleyat-Maurel

  2. Laboratoire de Statistiques et Probabilités, U.A. CNRS 745, Université Paul Sabatier, 118, Route de Narbonne, F-31062, Toulouse Cedex, France

    D. Michel

Authors
  1. M. Chaleyat-Maurel
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  2. D. Michel
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Chaleyat-Maurel, M., Michel, D. A Stroock Varadhan support theorem in non-linear filtering theory. Probab. Th. Rel. Fields 84, 119–139 (1990). https://doi.org/10.1007/BF01288562

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  • Received: 11 January 1988

  • Revised: 15 May 1989

  • Issue Date: March 1990

  • DOI: https://doi.org/10.1007/BF01288562

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Stochastic Process
  • Probability Theory
  • Diffusion Process
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