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Malliavin Calculus and Stochastic Analysis pp 115–138Cite as

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

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

MSC subject classifications 2010: 60F10; 60G15.

Received 9/23/2011; Accepted 3/5/2012; Final 3/20/2012

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References

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Acknowledgements

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

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Authors and Affiliations

  1. Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, 12489, Berlin, Germany

    Andreas Andresen, Peter Imkeller & Nicolas Perkowski

Authors
  1. Andreas Andresen
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  2. Peter Imkeller
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  3. Nicolas Perkowski
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Corresponding author

Correspondence to Peter Imkeller .

Editor information

Editors and Affiliations

  1. , Department of Statistics, Purdue University, North University Street 150, West Lafayette, 47907, Indiana, USA

    Frederi Viens

  2. , Department of Mathematics, University of Kansas, Jayhawk Blvd 1460, Lawrence, 66045, Kansas, USA

    Jin Feng

  3. Dept. Mathematics, University of Kansas, Snow Hall 405, Lawrence, 66045-2142, Kansas, USA

    Yaozhong Hu

  4. , Department of Economics and Business, University Pompeu Fabra, Ramon Trias Fargas 25-27, Barcelona, 08005, Spain

    Eulalia Nualart 

Additional information

Dedicated to David Nualart on the occasion of his 60th birthday

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Andresen, A., Imkeller, P., Perkowski, N. (2013). Large Deviations for Hilbert-Space-Valued Wiener Processes: A Sequence Space Approach. In: Viens, F., Feng, J., Hu, Y., Nualart , E. (eds) Malliavin Calculus and Stochastic Analysis. Springer Proceedings in Mathematics & Statistics, vol 34. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-5906-4_6

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