Concentration of the Brownian bridge on Cartan-Hadamard manifolds with pinched negative sectional curvature - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annales de l'Institut Fourier Année : 2005

Concentration of the Brownian bridge on Cartan-Hadamard manifolds with pinched negative sectional curvature

Résumé

We study the rate of concentration of a Brownian bridge in time one around the corresponding geodesical segment on a Cartan-Hadamard manifold with pinched negative sectional curvature, when the distance between the two extremities tends to infinity. This improves on previous results by A. Eberle, and one of us. Along the way, we derive a new asymptotic estimate for the logarithmic derivative of the heat kernel on such manifolds, in bounded time and with one space parameter tending to infinity, which can be viewed as a counterpart to Bismut's asymptotic formula in small time.
Fichier principal
Vignette du fichier
bbch.pdf (340.67 Ko) Télécharger le fichier

Dates et versions

hal-00002886 , version 1 (20-09-2004)
hal-00002886 , version 2 (20-09-2004)

Identifiants

Citer

Marc Arnaudon, Thomas Simon. Concentration of the Brownian bridge on Cartan-Hadamard manifolds with pinched negative sectional curvature. Annales de l'Institut Fourier, 2005, 55 (3), pp.891-930. ⟨hal-00002886v2⟩
105 Consultations
144 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More