Barycentres et martingales sur une variété
Brownian motion and random walks on manifolds
We develop a procedure that allows us to “descretise” the Brownian motion on a Riemannian manifold. We construct thus a random walk that is a good approximation of the Brownian motion.
Brownian motion and stereographic projection
Brownian motion and transient groups
In this paper I consider a covering of a Riemannian manifold . I prove that Green’s function exists on if any and only if the symmetric translation invariant random walks on the covering group are transient (under the assumption that is compact).
Brownian motion, excursions, and matrix factors
Brownian motion on a surface of negative curvature
Brownian motion on compact manifolds: cover time and late points.
Brownian motion with respect to time-changing riemannian metrics, applications to Ricci flow
We generalize brownian motion on a riemannian manifold to the case of a family of metrics which depends on time. Such questions are natural for equations like the heat equation with respect to time dependent laplacians (inhomogeneous diffusions). In this paper we are in particular interested in the Ricci flow which provides an intrinsic family of time dependent metrics. We give a notion of parallel transport along this brownian motion, and establish a generalization of the Dohrn–Guerra or damped...
Brownian motions in the diffeomorphism group I
Calcul des variations sur un brownien subordonné
Calcul stochastique avec sauts sur une variété
Canonical lift and exit law of the fundamental diffusion associated with a kleinian group
Caractéristiques locales des semi-martingales et changements de probabilités
Characterization of maximal Markovian couplings for diffusion processes.
Concentration of the Brownian bridge on Cartan-Hadamard manifolds with pinched negative sectional curvature
We study the rate of concentration of a Brownian bridge in time one around the corresponding geodesical segment on a Cartan-Hadamard manifold with pinched negative sectional curvature, when the distance between the two extremities tends to infinity. This improves on previous results by A. Eberle, and one of us . Along the way, we derive a new asymptotic estimate for the logarithmic derivative of the heat kernel on such manifolds, in bounded time and with one space parameter...
Conditional expectations for derivatives of certain stochastic flows
Conditions for global existence of solutions of ordinary differential, stochastic differential, and parabolic equations.
Connexions et martingales dans les groupes de Lie
Construction directe d'une diffusion sur une variété
Convergence des approximations de McShane d'une diffusion sur une variété compacte