On the Independence of Exit Time and Exit Position from Small Geodesic Balls for Brownian Motions on Riemannian Manifolds.
On the notion of -completeness of a stochastic flow on a manifold.
On the projections of Laplacians under Riemannian submersions.
On the relation between elliptic and parabolic Harnack inequalities
We show that, if a certain Sobolev inequality holds, then a scale-invariant elliptic Harnack inequality suffices to imply its a priori stronger parabolic counterpart. Neither the relative Sobolev inequality nor the elliptic Harnack inequality alone suffices to imply the parabolic Harnack inequality in question; both are necessary conditions. As an application, we show the equivalence between parabolic Harnack inequality for on , (i.e., for ) and elliptic Harnack inequality for on .
On two transfer principles in stochastic differential geometry
Opérateurs elliptiques et mesures sur l'espace des lacets invariants par le groupe des difféomorphismes du cercle
Optimal heat kernel bounds under logarithmic Sobolev inequalities
Optimal heat kernel bounds under logarithmic Sobolev inequalities
We establish optimal uniform upper estimates on heat kernels whose generators satisfy a logarithmic Sobolev inequality (or entropy-energy inequality) with the optimal constant of the Euclidean space. Off-diagonals estimates may also be obtained with however a smaller d istance involving harmonic functions. In the last part, we apply these methods to study some heat kernel decays for diffusion operators of the type Laplacian minus the gradient of a smooth potential with a given growth at infinity....
Poisson kernels of half-spaces in real hyperbolic spaces.
Pôles de la matrice de diffusion pour des perturbations captives
Problème de la glace pilée
Régularisation d'équations de Stratonovitch à sauts entre variétés
Relèvement horizontal d'une semimartingale càdlàg
Remarques sur la convergence des martingales dans les variétés
Riesz transforms for symmetric diffusion operators on complete Riemannian manifolds.
Rolling with “slipping” : I
Self-interacting diffusions II : convergence in law
Semimartingales in predictable random open sets
Sharp estimates of the Green function of hyperbolic Brownian motion
The main objective of the work is to provide sharp two-sided estimates of the λ-Green function, λ ≥ 0, of the hyperbolic Brownian motion of a half-space. We rely on the recent results obtained by K. Bogus and J. Małecki (2015), regarding precise estimates of the Bessel heat kernel for half-lines. We also substantially use the results of H. Matsumoto and M. Yor (2005) on distributions of exponential functionals of Brownian motion.
Shrinkage strategies in some multiple multi-factor dynamical systems
In this paper, we are interested in estimation problem for the drift parameters matrices of m independent multivariate diffusion processes. More specifically, we consider the case where the m-parameters matrices are supposed to satisfy some uncertain constraints. Given such an uncertainty, we develop shrinkage estimators which improve over the performance of the maximum likelihood estimator (MLE). Under an asymptotic distributional quadratic risk criterion, we study the relative dominance of the...