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Probability Theory and Related Fields

, Volume 115, Issue 4, pp 549–578 | Cite as

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

  • D. Crisan
  • T. Lyons

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 n¼. This paper is the third in a sequence, and represents the most efficient algorithm we have identified so far.

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • D. Crisan
    • 1
  • T. Lyons
    • 1
  1. 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.ukGB

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