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Malliavin calculus with time dependent coefficients and application to nonlinear filtering
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  • Published: June 1990

Malliavin calculus with time dependent coefficients and application to nonlinear filtering

  • Patrick Florchinger1 

Probability Theory and Related Fields volume 86, pages 203–223 (1990)Cite this article

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Summary

In this paper, we prove, using Malliavin calculus, that under a local Hörmander condition the solution of a stochastic differential equation with time depending coefficients admits aC ∞ density with respect to Lebesgue measure. An application of this result to nonlinear filtering is developed in this paper to prove the existence of aC ∞ density for the filter associated with a correlated system whose observation is one dimensional with unbounded coefficients.

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Authors and Affiliations

  1. U.R.A. C.N.R.S. No 399, Département de Mathématiques, U.F.R. M.I.M., Université de Metz, Ile du Saulcy, F-57045, Metz Cedex, France

    Patrick Florchinger

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  1. Patrick Florchinger
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Florchinger, P. Malliavin calculus with time dependent coefficients and application to nonlinear filtering. Probab. Th. Rel. Fields 86, 203–223 (1990). https://doi.org/10.1007/BF01474642

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  • Received: 11 July 1989

  • Revised: 03 January 1990

  • Issue Date: June 1990

  • DOI: https://doi.org/10.1007/BF01474642

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Keywords

  • Differential Equation
  • Stochastic Process
  • Probability Theory
  • Lebesgue Measure
  • Mathematical Biology
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