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Pinning class of the Wiener measure by a functional: related martingales and invariance properties
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  • Published: 04 July 2003

Pinning class of the Wiener measure by a functional: related martingales and invariance properties

  • Fabrice Baudoin1 &
  • Michèle Thieullen2 

Probability Theory and Related Fields volume 127, pages 1–36 (2003)Cite this article

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Abstract.

For a given functional Y on the path space, we define the pinning class of the Wiener measure as the class of probabilities which admit the same conditioning given Y as the Wiener measure. Using stochastic analysis and the theory of initial enlargement of filtration, we study the transformations (not necessarily adapted) which preserve this class. We prove, in this non Markov setting, a stochastic Newton equation and a stochastic Noether theorem. We conclude the paper with some non canonical representations of Brownian motion, closely related to our study.

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Author information

Authors and Affiliations

  1. Department of Financial and Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstrasse 8-10/105, 1040, Vienna, Austria

    Fabrice Baudoin

  2. Laboratoire de Probabilités et Modèles aléatoires, Université Paris 6, Boîte 188, 4 Place Jussieu, 75252, Paris Cédex 05, France

    Michèle Thieullen

Authors
  1. Fabrice Baudoin
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  2. Michèle Thieullen
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Corresponding author

Correspondence to Michèle Thieullen.

Additional information

Mathematics Subject Classification (2000): 60G44, 60H07, 60H20, 60H30

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Baudoin, F., Thieullen, M. Pinning class of the Wiener measure by a functional: related martingales and invariance properties. Probab. Theory Relat. Fields 127, 1–36 (2003). https://doi.org/10.1007/s00440-003-0280-4

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  • Received: 24 June 2002

  • Revised: 10 March 2003

  • Published: 04 July 2003

  • Issue Date: September 2003

  • DOI: https://doi.org/10.1007/s00440-003-0280-4

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Keywords

  • Conditioned stochastic differential equation
  • Initial enlargement of filtrations
  • Newton martingale
  • Noether stochastic theorem
  • Stochastic analysis
  • Symmetries in stochastic calculus
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