Dans une variété de Cartan-Hadamard à courbure négative pincée, nous déterminons la
concentration d’un pont brownien en temps
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.
Keywords: Brownian bridge, Cartan-Hadamard manifold, comparison theorems, Cox-Ingersoll-Ross process, heat kernel, large deviations, rank-one noncompact symmetric space
Mot clés : pont brownien, variété de Cartan-Hadamard, théorèmes de comparaison, processus de Cox-Ingersoll-Ross, noyau de la chaleur, grandes déviations, espace symétrique non compact de rang un
@article{AIF_2005__55_3_891_0, author = {Arnaudon, Marc and Simon, Thomas}, title = {Concentration of the {Brownian} bridge on {Cartan-Hadamard} manifolds with pinched negative sectional curvature}, journal = {Annales de l'Institut Fourier}, pages = {891--930}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {3}, year = {2005}, doi = {10.5802/aif.2117}, mrnumber = {2149406}, zbl = {1075.58019}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2117/} }
TY - JOUR AU - Arnaudon, Marc AU - Simon, Thomas TI - Concentration of the Brownian bridge on Cartan-Hadamard manifolds with pinched negative sectional curvature JO - Annales de l'Institut Fourier PY - 2005 SP - 891 EP - 930 VL - 55 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2117/ DO - 10.5802/aif.2117 LA - en ID - AIF_2005__55_3_891_0 ER -
%0 Journal Article %A Arnaudon, Marc %A Simon, Thomas %T Concentration of the Brownian bridge on Cartan-Hadamard manifolds with pinched negative sectional curvature %J Annales de l'Institut Fourier %D 2005 %P 891-930 %V 55 %N 3 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2117/ %R 10.5802/aif.2117 %G en %F AIF_2005__55_3_891_0
Arnaudon, Marc; Simon, Thomas. Concentration of the Brownian bridge on Cartan-Hadamard manifolds with pinched negative sectional curvature. Annales de l'Institut Fourier, Tome 55 (2005) no. 3, pp. 891-930. doi : 10.5802/aif.2117. http://www.numdam.org/articles/10.5802/aif.2117/
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