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Dévissage of a Poisson Boundary Under Equivariance and Regularity Conditions

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Séminaire de Probabilités XLVIII

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 2168))

Abstract

We present a method that allows, under suitable equivariance and regularity conditions, to determine the Poisson boundary of a diffusion starting from the Poisson boundary of a sub-diffusion of the original one. We then give two examples of application of this dévissage method. Namely, we first recover the classical result that the Poisson boundary of Brownian motion on a rotationally symmetric manifolds is generated by its escape angle, and we then give an “elementary” probabilistic proof of the delicate result of Bailleul (Probab Theory Relat Fields 141(1–2):283-329, 2008), i.e. the determination of the Poisson boundary of the relativistic Brownian motion in Minkowski space-time.

MSC Classification: 60J45, 60J60, 53C30, 58D19

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Author information

Authors and Affiliations

  1. IRMAR, Université de Rennes 1, Rennes, France

    Jürgen Angst

  2. LPMA, Université Pierre et Marie Curie, Paris, France

    Camille Tardif

Authors
  1. Jürgen Angst
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  2. Camille Tardif
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Corresponding author

Correspondence to Jürgen Angst .

Editor information

Editors and Affiliations

  1. Laboratoire de Mathématiques, Université de Versailles-St Quentin, Versailles , France

    Catherine Donati-Martin

  2. Campus scientifique, IECL, Vandoeuvre-les-Nancy CEDEX, France

    Antoine Lejay

  3. Laboratoire de Mathématiques, Université de Versailles-St Quentin, Versailles, France

    Alain Rouault

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Angst, J., Tardif, C. (2016). Dévissage of a Poisson Boundary Under Equivariance and Regularity Conditions. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLVIII. Lecture Notes in Mathematics(), vol 2168. Springer, Cham. https://doi.org/10.1007/978-3-319-44465-9_8

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