We consider a multidimensional diffusion process (X^\alpha_t)_0≦t≦T whose dynamics
depends on a parameter α. Our first purpose is to write as an expectation the sensitivity …

We prove a variational principle for stochastic flows on manifolds. It extends VI Arnoldʼs
description of Lagrangian Euler flows, which are geodesics for the L 2 metric on the …

We define horizontal diffusion in C 1 path space over a Riemannian manifold and prove its
existence. If the metric on the manifold is developing under the forward Ricci flow, horizontal …

We provide a theory of manifold‐valued rough paths of bounded 3> p 3>p‐variation, which
we do not assume to be geometric. Rough paths are defined in charts, relying on the vector …

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 …

Résumé On écrit une formule de Bismut intrinsèque pour la hessienne d'un semigroupe de
la chaleur ou d'une fonction harmonique sur une variété, en calculant des dérivées …

We construct a family of SDEs with smooth coefficients whose solutions select a reflected
Brownian flow as well as a corresponding stochastic damped transport process (W_t), the …

We construct a parallel transport U in a vector bundle E, along the paths of a Brownian
motion in the underlying manifold, with respect to a time dependent covariant derivative∇ …

Basic derivative formulas are presented for hypoelliptic heat semigroups and harmonic
functions extending earlier work in the elliptic case. According to our approach, special …

Differentiable families of∇-martingales on manifolds are investigated: their infinitesimal
variation provides a notion of stochastic Jacobi fields. Such objects are known [2] to be …