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Filtration des ponts browniens et equations differentielles stochastiques lineaires

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Séminaire de Probabilités XXIV 1988/89

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1426))

Abstract

In this paper, we associate to a one-dimensional Brownian motion (Xt)t≥0, starting from 0, another Brownian motion:

. We remark that, for every t>0, σ(, s≤t) coïncides, up to negligible sets, with the σ-field generated by the Brownian bridge

. We study the ergodic properties of the application : , which preserves the Wiener measure. The Laguerre polynomials play an essential role in this study.

More generally, we study the filtration of the process

for a large class of functions φ, which may have some singularity at 0.

Finally, given a Brownian motion (Bt)t≥0, we study the properties of all solutions of:

thus completing results obtained earlier by Chitashvili-Toronjadze [2].

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References

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Author information

Authors and Affiliations

  1. UFR de Mathématiques, Université Paris 7, Tour 45–55, 5ème étage, 2, place Jussieu, 75251, Paris Cédex 05

    T. Jeulin

  2. Laboratoire de Probabilités, Université P. et M. Curie, Tour 56, 3ème étage, 4, Place Jussieu, 75252, Paris Cédex 05

    M. Yor

Authors
  1. T. Jeulin
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  2. M. Yor
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Editor information

Jacques Azéma Marc Yor Paul André Meyer

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© 1990 Springer-Verlag

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Jeulin, T., Yor, M. (1990). Filtration des ponts browniens et equations differentielles stochastiques lineaires. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXIV 1988/89. Lecture Notes in Mathematics, vol 1426. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083768

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  • DOI: https://doi.org/10.1007/BFb0083768

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52694-0

  • Online ISBN: 978-3-540-47098-4

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