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math.PR2009★ 7 cited
Horizontal diffusion in path space
Marc Arnaudon, Abdoulaye Koléhè Coulibaly-Pasquier, Anton Thalmaier
We define horizontal diffusion in path space over a Riemannian manifold and prove its existence. If the metric on the manifold is developing under the forward Ricci flow, hor…
math.PR2009
Li-Yau Type Gradient Estimates and Harnack Inequalities by Stochastic Analysis
Marc Arnaudon, Anton Thalmaier
In this paper we use methods from Stochastic Analysis to establish Li-Yau type estimates for positive solutions of the heat equation. In particular, we want to emphasize that Stoch…