[Calcul de variations stochastiques et l'inéqualité de Harnack sur l'espace de chemins riemanniens]
On décrit l'espace tangent à l'espace de chemins riemanniens comme un espace de processus tangents localisé sur des fueuilles browniennes ; le fibré de repères adaptés sur l'espace de chemins riemanniens et son équation de structure sont donnés. Le calcul de variations stochastiques permet de dériver l'inégalité de Harnack–Bismut pour le semigroupe de Norris.
We describe the tangent space of Riemannian path space as a space of tangent processes localized on Brownian sheets; the bundle of adapted frames above a Riemannian path space and its structural equation are given. The stochastic calculus of variations allows us to derive Harnack–Bismut inequality for the Norris semigroup.
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@article{CRMATH_2002__335_10_817_0,
author = {Cruzeiro, Ana-Bela and Malliavin, Paul},
title = {Stochastic calculus of variations and {Harnack} inequality on {Riemannian} path spaces},
journal = {Comptes Rendus. Math\'ematique},
pages = {817--820},
publisher = {Elsevier},
volume = {335},
number = {10},
year = {2002},
doi = {10.1016/S1631-073X(02)02561-X},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02561-X/}
}
TY - JOUR AU - Cruzeiro, Ana-Bela AU - Malliavin, Paul TI - Stochastic calculus of variations and Harnack inequality on Riemannian path spaces JO - Comptes Rendus. Mathématique PY - 2002 SP - 817 EP - 820 VL - 335 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02561-X/ DO - 10.1016/S1631-073X(02)02561-X LA - en ID - CRMATH_2002__335_10_817_0 ER -
%0 Journal Article %A Cruzeiro, Ana-Bela %A Malliavin, Paul %T Stochastic calculus of variations and Harnack inequality on Riemannian path spaces %J Comptes Rendus. Mathématique %D 2002 %P 817-820 %V 335 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02561-X/ %R 10.1016/S1631-073X(02)02561-X %G en %F CRMATH_2002__335_10_817_0
Cruzeiro, Ana-Bela; Malliavin, Paul. Stochastic calculus of variations and Harnack inequality on Riemannian path spaces. Comptes Rendus. Mathématique, Tome 335 (2002) no. 10, pp. 817-820. doi : 10.1016/S1631-073X(02)02561-X. http://www.numdam.org/articles/10.1016/S1631-073X(02)02561-X/
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