Le théorème de convergence des martingales dans les variétés riemanniennes d'après R.W. Darling et W.A. Zheng
Lévy processes, pseudo-differential operators and Dirichlet forms in the Heisenberg group
Limiting angle of brownian motion in certain two-dimensional Cartan-Hadamard manifolds
Limiting behaviors of the Brownian motions on hyperbolic spaces
Using explicit representations of the Brownian motions on hyperbolic spaces, we show that their almost sure convergence and the central limit theorems for the radial components as time tends to infinity can be easily obtained. We also give a straightforward strategy to obtain explicit expressions for the limit distributions or Poisson kernels.
Local Fatou theorem and the density of energy on manifolds of negative curvature.
Local property of Dirichlet forms and diffusions on general state spaces.
Malliavin Calculus for a general manifold
Martin boundary for homogeneous riemannian manifolds of negative curvature at the bottom of the spectrum.
In this paper we treat noncoercive operators on simply connected homogeneous manifolds of negative curvature.
Martingales in manifolds. Definition, examples and behaviour under maps
Martingales on noncompact manifolds : maximal inequalities and prescribed limits
Mean-value theorems and ergodicity of certain geodesic random walks
Non-Divergence From Operators and Variations on Yau's Explosion Criterion.
Non-symmetric approximations for manifold-valued semimartingales
Note rectificative : “Asymptotic winding of the geodesic flow on modular surfaces and continuous fractions”
On differential equations and inclusions with mean derivatives on a compact manifold
We introduce and investigate a new sort of stochastic differential inclusions on manifolds, given in terms of mean derivatives of a stochastic process, introduced by Nelson for the needs of the so called stochastic mechanics. This class of stochastic inclusions is ideologically the closest one to ordinary differential inclusions. For inclusions with forward mean derivatives on manifolds we prove some results on the existence of solutions.
On Gromov's theorem and -Hodge decomposition.
On non-euclidean harmonic measure
On Probalistic Commutative Spaces.
On recent progress for the stochastic Navier Stokes equations
We give an overview of the ideas central to some recent developments in the ergodic theory of the stochastically forced Navier Stokes equations and other dissipative stochastic partial differential equations. Since our desire is to make the core ideas clear, we will mostly work with a specific example : the stochastically forced Navier Stokes equations. To further clarify ideas, we will also examine in detail a toy problem. A few general theorems are given. Spatial regularity, ergodicity, exponential...
On the Dirichlet Problem at Infinity for Manifolds of Nonpositive Curvature.