Continuous Maassen kernels and the inverse oscillator
Convergence of stochastic flows with jumps and Levy processes in diffeomorphisms group
Correction : “On two transfer principles in stochastic differential geometry”
De Rham-Hodge-Kodaira decomposition in ...-dimensions.
Développement asymptotique du noyau de la chaleur hypoelliptique hors du cut-locus
Développement des distributions suivant les chaos de Wiener et applications à l'analyse stochastique
Diffeomorphisms of the circle and the based stochastic loop space
Différentiabilité fine, différentiabilité stochastique, différentiabilité stochastique de fonctions finement harmoniques
Dans ce travail, nous définissons et étudions la notion de “différentiabilité stochastique” d’une fonction définie sur un ouvert fin d’une variété riemannienne de dimension finie. Nous démontrons ensuite qu’une fonction admettant une “suite d’approximation forte” est, quasi-partout, stochastiquement indéfiniment différentiable et nous appliquons ces résultats à une classe de fonctions finement harmoniques.
Differential equations driven by gaussian signals
We consider multi-dimensional gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of Lévy area(s). gaussian rough paths are constructed with a variety of weak and strong approximation results. Together with a new RKHS embedding, we obtain a powerful – yet conceptually simple – framework in which to analyze differential equations driven by gaussian signals in the rough paths sense.
Differential equations of stochastic processes which have derivative in quadratic mean
Dirichlet functions of reflected Brownian motion
We give a complete analytical characterization of the functions transforming reflected Brownian motions to local Dirichlet processes.
Distributions sur l'espace de P. Lévy et calcul stochastique
Équations différentielles stochastiques lipschitziennes
Espaces de Fock pour les processus de Wiener et de Poisson
Euler's Approximations of Solutions of Reflecting SDEs with Discontinuous Coefficients
Let D be either a convex domain in or a domain satisfying the conditions (A) and (B) considered by Lions and Sznitman (1984) and Saisho (1987). We investigate convergence in law as well as in for the Euler and Euler-Peano schemes for stochastic differential equations in D with normal reflection at the boundary. The coefficients are measurable, continuous almost everywhere with respect to the Lebesgue measure, and the diffusion coefficient may degenerate on some subsets of the domain.
Euler's Approximations of Weak Solutions of Reflecting SDEs with Discontinuous Coefficients
We study convergence in law for the Euler and Euler-Peano schemes for stochastic differential equations reflecting on the boundary of a general convex domain. We assume that the coefficients are measurable and continuous almost everywhere with respect to the Lebesgue measure. The proofs are based on new estimates of Krylov's type for the approximations considered.
Exponential asymptotic stability of linear Itô-Volterra equations with damped stochastic perturbations.
Finite dimensional determinants as characteristic functions of quadratic Wiener functionals.
Fonctionnelles browniennes généralisées intégrale de Feynman
Formule de composition pour une classe d'opérateurs