An invariance principle for martingales with values in sobolev spaces

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)


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].


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. ALDOUS.— Stopping times and tightness.— Ann. of Prob. 6, no 2, 1978, 335–40.Google Scholar
  2. [2]
    L. ARNOLD.— Mathematical models of chemical reactions. in: Stochastic systems. (ed.) M. Hazewinkel, J. Willems. Dordrecht, 1981.Google Scholar
  3. [3]
    L. ARNOLD, M. THEODOSOPULU.— Deterministic limit of the stochastic model of chemical reactions with diffusion. Adv. Appl. Prob. 12, 1980.Google Scholar
  4. [4]
    P. KOTELENEZ.— Law of large numbers and central limit theorem for chemical reactions with diffusions. Universität Bremen, 1982.Google Scholar
  5. [5]
    E. LENGLART.—Relations de domination entre deux processus. Ann. Inst. H. Poincaré, B XIII, 1977, 171–179.Google Scholar
  6. [6]
    M. METIVIER.— Semimartingales. De Gruyter ed. Berlin, New York, 1982.Google Scholar
  7. [7]
    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
  8. [8]
    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

  1. 1.Ecole PolytechniquePalaiseau Cedex

Personalised recommendations