Stochastic calculus of variations and Harnack inequality on Riemannian path spaces
[Calcul de variations stochastiques et l'inéqualité de Harnack sur l'espace de chemins riemanniens]
Comptes Rendus. Mathématique, Tome 335 (2002) no. 10, pp. 817-820.

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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DOI : 10.1016/S1631-073X(02)02561-X
Cruzeiro, Ana-Bela 1 ; Malliavin, Paul 2

1 Dep. Matemática I.S.T. and Grupo de Física-Matemática U.L., Av. Rovisco Pais, 1049-001 Lisboa, Portugal
2 10, rue Saint Louis en l'Isle, 75004 Paris, France
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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://archive.numdam.org/articles/10.1016/S1631-073X(02)02561-X/

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