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An invariance principle for martingales with values in sobolev spaces

  • Michel Metivier
Fluctuations And Asymptotic Analysis Of Finite And Infinite Dimensional Systems
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 69)

Abstract

Starting with an example occuring in the modeling of a chemical reaction we introduce a wide class of situations where one has to study the convergence in law of an "accompanying martingale" taking its values in a Sobolev space.

We present a sufficient condition for tightness and an "invariance principle", stating only the results, the proofs of which will be exposed in detail in a subsequent paper [7].

Keywords

Hilbert Space Sobolev Space Invariance Principle Local Martingale Complete Orthonormal System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    M. METIVIER.— Convergence faible et principe d'invariance pour des martingales à valeurs dans des espaces de Sobolev. To appear in Ann. Inst. H. Poincaré.Google Scholar
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    R. REBOLLEDO.— La méthode des martingales appliquée à la convergence en loi des processus. Mémoires de la S.M.F. no 62, 1979.Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Michel Metivier
    • 1
  1. 1.Ecole PolytechniquePalaiseau Cedex

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