Stochastic calculus of variations and Harnack inequality on Riemannian path spaces

Abstract

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. To cite this article: A.-B. Cruzeiro, P. Malliavin, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 817–820.