19 citations · 41 across the 10 of their papers we have counts for
3 papers · 1 filter
Existence of non-trivial harmonic functions on Cartan-Hadamard manifolds of unbounded curvature
Marc Arnaudon, Anton Thalmaier, Stefanie Ulsamer
The Liouville property of a complete Riemannian manifold (i.e., the question whether there exist non-trivial bounded harmonic functions) attracted a lot of attention. For Cartan-Ha…
Gradient Estimate and Harnack Inequality on Non-Compact Riemannian Manifolds
Marc Arnaudon, Anton Thalmaier, Feng-Yu Wang
A new type of gradient estimate is established for diffusion semigroups on non-compact complete Riemannian manifolds. As applications, a global Harnack inequality with power and a…
Convex ordering for random vectors using predictable representation
Marc Arnaudon, Jean-Christophe Breton, Nicolas Privault
We prove convex ordering results for random vectors admitting a predictable representation in terms of a Brownian motion and a non-necessarily independent jump component. Our metho…