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Filtering and Control of Random Processes pp 294–313Cite as

Efficient numerical schemes for the approximation of expectations of functionals of the solution of a S.D.E., and applications

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 61))

Abstract

This paper presents results appearing in Talay [8], and show their possible applications in non linear filtering in particular. We develop a method to approximate expectations of functionals of the solution of a S.D.E.; this method is efficiently implementable on a computer, and is based on both Monte-Carlo methods and discretizations of S.D.E. Convergence is shown and bounds of the error are given.

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References

  1. I. GIKHMAN & A. SHOROKHOD — "Introduction à la théorie des processus aléatoires" — Ed. Mir — (1980)

    Google Scholar 

  2. P. HENRICI — "Discrete Variable Methods in Ordinary Differential Equations" — Wiley (1962).

    Google Scholar 

  3. H. KUNITA — Stochastic Differential Equations and Stochastic flows of Diffeomorphims — Cours de l'Ecole d'Eté de Probalites de Saint-Flour 1982 — To appear in "Lecture Notes in Mathematics", Springer — Verlag.

    Google Scholar 

  4. G.N. MILSHTEIN — A Method of Second Order Accuracy integration of S.D.E. — Theory Proba. Appl. 23, pp 396–401 (1976).

    Google Scholar 

  5. E. PARDOUX — Equations du Filtrage non linéaire, de la Prédiction et du Lissage — Stochastics, vol. 6, pp 193–231 (1982).

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  6. E. PARDOUX & D. TALAY — Approximation and Simulation of Solutions of S.D.E. — to appear in Acta Applicandae Mathematicae (1984).

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  7. R.Y. RUBINSTEIN — "Simulation and the Monte-Carlo method" Wiley (1981)

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  8. D. TALAY — "Discretisation d'une E.D.S. et calcul approché d'espérances de fonctionnelles de la solution". (à paraître).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Inria Sophia-Antipolis, 06560, Valbonne, France

    Denis Talay

Authors
  1. Denis Talay
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Editor information

Hayri Korezlioglu Gérald Mazziotto Jacques Szpirglas

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© 1984 Springer-Verlag

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Talay, D. (1984). Efficient numerical schemes for the approximation of expectations of functionals of the solution of a S.D.E., and applications. In: Korezlioglu, H., Mazziotto, G., Szpirglas, J. (eds) Filtering and Control of Random Processes. Lecture Notes in Control and Information Sciences, vol 61. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006577

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  • DOI: https://doi.org/10.1007/BFb0006577

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13270-7

  • Online ISBN: 978-3-540-38832-6

  • eBook Packages: Springer Book Archive

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