Géométrie différentielle stochastique, II
Géométrie stochastique sans larmes, I
Geometry of non-holonomic diffusion
We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint distribution. For -Chaplygin systems, this yields a stochastic criterion for the existence of a smooth preserved measure. As an application of our results we consider the motion planning problem for the noisy two-wheeled robot and the noisy snakeboard.
Geometry of stochastic delay differential equations.
Harmonic analysis on fractal spaces
Harmonic functions on loop groups
Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions.
Heat kernel bounds on manifolds.
Heat kernel on manifolds with ends
We prove two-sided estimates of heat kernels on non-parabolic Riemannian manifolds with ends, assuming that the heat kernel on each end separately satisfies the Li-Yau estimate.
Homotopy and Homology Vanishing Theorems and the Stability of Stochastic Flows.
Horizontal martingales in vector bundles
Inégalités de Sobolev faibles : un critère
Intrinsic location parameter of a diffusion process.
Introduction aux méthodes euclidiennes en théorie quantique des champs
Invariant measure for some differential operators and unitarizing measure for the representation of a Lie group. Examples in finite dimension
Consider a Lie group with a unitary representation into a space of holomorphic functions defined on a domain 𝓓 of ℂ and in L²(μ), the measure μ being the unitarizing measure of the representation. On finite-dimensional examples, we show that this unitarizing measure is also the invariant measure for some differential operators on 𝓓. We calculate these operators and we develop the concepts of unitarizing measure and invariant measure for an OU operator (differential operator associated to...
Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds
L¹-convergence and hypercontractivity of diffusion semigroups on manifolds
Let be the Markov semigroup generated by a weighted Laplace operator on a Riemannian manifold, with μ an invariant probability measure. If the curvature associated with the generator is bounded below, then the exponential convergence of in L¹(μ) implies its hypercontractivity. Consequently, under this curvature condition L¹-convergence is a property stronger than hypercontractivity but weaker than ultracontractivity. Two examples are presented to show that in general, however, L¹-convergence...
La propriété de sous-harmonicité des diffusions dans les variétés
Large time estimates for non-symmetric heat kernel on the affine group
Le principe du maximum et l'hypoellipticité globale