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Particle approximation for first order stochastic partial differential equations

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Applied Stochastic Analysis

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 177))

Abstract

A class of degenerate second order stochastic PDE is considered, for which a representation result in terms of stochastic characteristics has been proved by Krylov-Rozovskii [2] and Kunita [3,4]. An example of a stochastic PDE in this class has been exhibited in Florchinger-LeGland.

Research partially supported by USACCE under Contract DAJA45-90-C-0008.

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References

  1. P. FLORCHINGER and F. LE GLAND, Time-discretization of the Zakai equation for diffusion processes observed in correlated noise, Stochastics and Stochastics Reports 35 (4) 233–256 (1991).

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  2. N.V. KRYLOV and B.L. ROZOVSKII, Characteristics of degenerating second-order parabolic Itô equations, J. Soviet Math. 32 (4) 336–348 (1982).

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  3. H. KUNITA, Stochastic partial differential equations connected with nonlinear filtering, in: Nonlinear Filtering and Stochastic Control (Cortona-1981) (eds. S.K.Mitter and A.Moro) 100–169, Springer-Verlag (LNM-972) (1982).

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  4. H. KUNITA, First order partial differential equations, in: Stochastic Analysis (Katata and Kyoto-1982) (ed. K.Itô) 249–269, North-Holland (1984).

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  5. H. KUNITA, Stochastic Flows and Stochastic Differential Equations, Cambridge University Press (1990).

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  6. P.A. RAVIART, An analysis of particle methods, in: Numerical Methods in Fluid Dynamics (Como-1983) (ed. F.Brezzi) 243–324, Springer-Verlag (LNM-1127) (1985).

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Author information

Authors and Affiliations

  1. Département de Mathématiques URA CNRS 399, Université de Metz, Ile du Saulcy, F-57045, Metz Cédex

    Patrick Florchinger

  2. INRIA Lorraine, CESCOM, Technopole de Metz 2000, 4 rue Marconi, F-57070, Metz

    François Le Gland

  3. INRIA Sophia-Antipolis Route des Lucioles, F-06565, Valbonne Cédex

    Patrick Florchinger

Authors
  1. Patrick Florchinger
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  2. François Le Gland
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Editor information

Ioannis Karatzas Daniel Ocone

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© 1992 Springer-Verlag

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Florchinger, P., Le Gland, F. (1992). Particle approximation for first order stochastic partial differential equations. In: Karatzas, I., Ocone, D. (eds) Applied Stochastic Analysis. Lecture Notes in Control and Information Sciences, vol 177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007052

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  • DOI: https://doi.org/10.1007/BFb0007052

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55296-3

  • Online ISBN: 978-3-540-47017-5

  • eBook Packages: Springer Book Archive

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