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The Onsager-Machlup functional for a class of anticipating processes
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  • Published: June 1992

The Onsager-Machlup functional for a class of anticipating processes

  • Mireille Chaleyat-Maurel1 &
  • David Nualart2 

Probability Theory and Related Fields volume 94, pages 247–270 (1992)Cite this article

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  • 2 Citations

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Summary

Consider the solution {X t , 0≦t≦1} of the equation

$$X_t = X_0 + W_t + \mathop \smallint \limits_0^t b(X_s ) d s,$$

whereW={W t , 0≦t≦1} is ad-dimensional Wiener process,b is a Lipschitz function from ℝd into ℝd, andX 0 is ad-dimensional functional of the Wiener process.

Under some additional hypotheses onX 0 andb, the Onsager-Machlup functional associated with the anticipating processX is determined with the help of a noncausal version of the Girsanov theorem due to S. Kusuoka.

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References

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Author information

Authors and Affiliations

  1. Laboratoire de Probabilités, Université de Paris VI, 4, Place Jussieu, F-75230, Paris, France

    Mireille Chaleyat-Maurel

  2. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, E-08007, Barcelona, Spain

    David Nualart

Authors
  1. Mireille Chaleyat-Maurel
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  2. David Nualart
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Additional information

The work of D. Naulart was done during a visit to the Laboratoire de Probabilités

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Cite this article

Chaleyat-Maurel, M., Nualart, D. The Onsager-Machlup functional for a class of anticipating processes. Probab. Th. Rel. Fields 94, 247–270 (1992). https://doi.org/10.1007/BF01192445

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  • Received: 22 January 1992

  • Revised: 15 April 1992

  • Issue Date: June 1992

  • DOI: https://doi.org/10.1007/BF01192445

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Mathematics Subject Classifications

  • 60H07
  • 60H10
  • 60J65
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