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Large Deviations for Hilbert-Space-Valued Wiener Processes: A Sequence Space Approach

Conference paper
First Online:
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 34)

Abstract

Ciesielski’s isomorphism between the space of α-Hölder continuous functions and the space of bounded sequences is used to give an alternative proof of the large deviation principle (LDP) for Wiener processes with values in Hilbert space.

Keywords

Large deviations Schilder’s theorem Hilbert space valued Wiener process Ciesielski’s isomorphism 
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Notes

Acknowledgements

Nicolas Perkowski is supported by a Ph.D. scholarship of the Berlin Mathematical School.

References

  1. 1.
    Baldi, P., Roynette, B.: Some exact equivalents for the Brownian motion in Hölder norm. Probab. Theory Relat. Fields 93, 457–484 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Ben Arous, G., Gradinaru, M.: Hölder norms and the support theorem for diffusions. Ann. Inst. H. Poincaré 30, 415–436 (1994)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Ben Arous, G., Ledoux, M.: Grandes déviations de Freidlin-Wentzell en norme Hölderienne. Séminaire de Probabilités 28, 293–299 (1994)MathSciNetGoogle Scholar
  4. 4.
    Ciesielski, Z.: On the isomorphisms of the spaces H α and m. Bull. Acad. Pol. Sci. 8, 217–222 (1960)Google Scholar
  5. 5.
    Da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions. Cambridge University Press, Cambridge (1992)zbMATHCrossRefGoogle Scholar
  6. 6.
    Dembo, A., Zeitouni, O.: Large Deviation Techniques and Applications. Springer, New York (1998)CrossRefGoogle Scholar
  7. 7.
    Eddahbi, M., Ouknine, Y.: Large deviations of diffusions on Besov-Orlicz spaces. Bull. Sci. Math. 121, 573–584 (1997)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Eddahbi, M., N’zi, M., Ouknine, Y.: Grandes déviations des diffusions sue les espaces de Besov-Orlicz et application. Stoch. Stoch. Rep. 65, 299–315 (1999)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Freidlin, M., Wentzell, A.: Random Perturbations of Dynamical Systems, 2nd edn. Springer, New York (1998)zbMATHCrossRefGoogle Scholar
  10. 10.
    Galves, A., Olivieri, E., Vares, M.: Metastability for a class of dynamical systems subject to small random perturbations. Ann. Probab. 15, 1288–1305 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Schilder, M.: Asymptotic formulas for Wiener integrals. Trans. Amer. Math. Soc. 125, 63–85 (1966)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany

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