Maximal Brownian motions

Autor: Michel Émery, Christophe Leuridan, Jean Brossard
Přispěvatelé: Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
Jazyk: angličtina
Rok vydání: 2009
Předmět:
Zdroj: Ann. Inst. H. Poincaré Probab. Statist. 45, no. 3 (2009), 876-886
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2009, 45 (3), pp.876-886. ⟨10.1214/08-AIHP194⟩
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2009, 45 (3), pp.876-886. ⟨10.1214/08-AIHP194⟩
ISSN: 0246-0203
1778-7017
DOI: 10.1214/08-AIHP194⟩
Popis: Let Z=(X, Y) be a planar Brownian motion, $\mathcal{Z}$ the filtration it generates, and B a linear Brownian motion in the filtration $\mathcal{Z}$. One says that B (or its filtration) is maximal if no other linear $\mathcal{Z}$-Brownian motion has a filtration strictly bigger than that of B. For instance, it is shown in [In Séminaire de Probabilités XLI 265–278 (2008) Springer] that B is maximal if there exists a linear Brownian motion C independent of B and such that the planar Brownian motion (B, C) generates the same filtration $\mathcal{Z}$ as Z. We do not know if this sufficient condition for maximality is also necessary. ¶ We give a necessary condition for B to be maximal, and a sufficient condition which may be weaker than the existence of such a C. This sufficient condition is used to prove that the linear Brownian motion ∫(X dY−Y dX)/|Z|, which governs the angular part of Z, is maximal.
Databáze: OpenAIRE
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