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Hypoelliptic non-homogeneous diffusions
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  • Published: August 2002

Hypoelliptic non-homogeneous diffusions

  • Patrick Cattiaux1 &
  • Laurent Mesnager2 

Probability Theory and Related Fields volume 123, pages 453–483 (2002)Cite this article

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Abstract.

 Let be a time dependent second order operator, written in usual or Hörmander form. We study the regularity of the law of the associated non-homogeneous (time dependent) diffusion process, under Hörmander's like conditions. Coefficients are only Hölder continuous in time. The main tool is Malliavin calculus. Our results extend and correct previous ones ([17] and related works, [15]). Related topics like filtering theory, killed or reflected processes, parabolic hypoellipticity are also discussed.

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Authors and Affiliations

  1. Ecole Polytechnique, CMAP, F-91128 Palaiseau Cedex, France. e-mail: cattiaux@@cmapx.polytechnique.fr, , , , , , FR

    Patrick Cattiaux

  2. Modal'X, Université de Paris X, UFR SEGMI, 200 avenue de laRépublique, F-92001 Nanterre Cedex, France. e-mail: mesnager@@modalx.u-paris10.fr, , , , , , FR

    Laurent Mesnager

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  1. Patrick Cattiaux
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  2. Laurent Mesnager
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Received: October 1999/Revised version: 12 November 2001 / Published online: 1 July 2002

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Cattiaux, P., Mesnager, L. Hypoelliptic non-homogeneous diffusions. Probab Theory Relat Fields 123, 453–483 (2002). https://doi.org/10.1007/s004400100194

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  • Issue Date: August 2002

  • DOI: https://doi.org/10.1007/s004400100194

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