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A particle approximation of the solution of the Kushner–Stratonovitch equation
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  • Published: November 1999

A particle approximation of the solution of the Kushner–Stratonovitch equation

  • D. Crisan1 &
  • T. Lyons1 

Probability Theory and Related Fields volume 115, pages 549–578 (1999)Cite this article

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Abstract.

We construct a sequence of branching particle systems α n convergent in measure to the solution of the Kushner–Stratonovitch equation. The algorithm based on this result can be used to solve numerically the filtering problem. We prove that the rate of convergence of the algorithm is of order n ¼. This paper is the third in a sequence, and represents the most efficient algorithm we have identified so far.

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Authors and Affiliations

  1. Department of Mathematics, Imperial College, 180 Queens Gate, London, SW7 2BZ, UK e-mail: D.Crisan@statslab.cam.ac.uk; t.lyons@ic.ac.uk, , , , , , GB

    D. Crisan & T. Lyons

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  1. D. Crisan
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  2. T. Lyons
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Received: 4 February 1997 / Revised version: 26 October 1998

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Cite this article

Crisan, D., Lyons, T. A particle approximation of the solution of the Kushner–Stratonovitch equation. Probab Theory Relat Fields 115, 549–578 (1999). https://doi.org/10.1007/s004400050249

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  • Issue Date: November 1999

  • DOI: https://doi.org/10.1007/s004400050249

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  • Mathematics Subject Classification (1991): 93E11, 60G57, 65U05
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