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Chapitre d'ouvrage Année : 2016

Dévissage of a Poisson boundary under equivariance and regularity conditions

Résumé

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 [Bai08], i.e. the determination of the Poisson boundary of the relativistic Brownian motion in Minkowski space-time.
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Dates et versions

hal-00951900, version 1 (25-02-2014)

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Jürgen Angst, Camille Tardif. Dévissage of a Poisson boundary under equivariance and regularity conditions. Catherine Donati-Martin; Antoine Lejay; Alain Rouault. Séminaire de Probabilités XLVII, 2168, Springer, pp.199-229, 2016, Lecture Notes in Mathematics, 978-3-319-44464-2. ⟨10.1007/978-3-319-44465-9_8⟩. ⟨hal-00951900⟩
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Dernière date de mise à jour le 26/06/2024
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