5 papers
Large time behaviour for the semigroup of the kinetic Brownian motion in the plane
Magalie Bénéfice, Michel Bonnefont, Marc Arnaudon +1
We establish an integration by parts formula for the semi-group in time of the kinetic Brownian motion in the Euclidean plane together with its speed in the circle. The sto…
Martingales On A Euclidean Manifold With A Boundary And Reflected BSDES In Non-Convex Domains
Marc Arnaudon, Jean-François Chassagneux, Sergey Nadtochiy +1
The purpose of this paper is twofold. First, we introduce the notion of a -martingale on a Euclidean manifold with a boundary (i.e., the closure of an open connected domain in…
Continuous-time filtering in Lie groups: estimation via the Fr{é}chet mean of solutions to stochastic differential equations
Magalie Bénéfice, Marc Arnaudon, Audrey Giremus
We compute the Fréchet mean of the solution to a continuous-time stochastic differential equation in a Lie group. It provides an estimator with minimal var…
Coarse Ricci curvature of weighted Riemannian manifolds
Marc Arnaudon, Xue-Mei Li, Benedikt Petko
We show that the generalized Ricci tensor of a weighted complete Riemannian manifold can be retrieved asymptotically from a scaled metric derivative of Wasserstein 1-distances betw…
Coarse extrinsic curvature of Riemannian submanifolds
Marc Arnaudon, Xue-Mei Li, Benedikt Petko
We introduce a novel concept of coarse extrinsic curvature for Riemannian submanifolds, inspired by Ollivier's notion of coarse Ricci curvature. This curvature is derived from the…