Stochastic calculus of variations and Harnack inequality on Riemannian path spaces (Q1851446)

The authors describe the tangent space of Riemannian path space as a space of tangent processes localized on Brownian sheets. This generalizes some constructions connected with the so called Markovian connection on the orthonormal frame bundle. The bundle of adapted frames over a Riemannian path space and its structural equation are described. Harnack-Bismut inequality for the Norris semigroup is derived by the use of stochastic calculus of variations.