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
Different approaches to stochastic parabolic differential equations
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.
Différentiabilité stochastique des fonctions finement harmoniques.
Differential equations driven by fractional Brownian motion.
A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.
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 driven by rough signals.
This paper aims to provide a systematic approach to the treatment of differential equations of the typedyt = Σi fi(yt) dxti where the driving signal xt is a rough path. Such equations are very common and occur particularly frequently in probability where the driving signal might be a vector valued Brownian motion, semi-martingale or similar process.However, our approach is deterministic, is totally independent of probability and permits much rougher paths than the Brownian paths usually discussed....
Differential equations of stochastic processes which have derivative in quadratic mean
Differential properties of measures on infinite dimensional spaces and the Malliavin calculus
Differentiation of measures.
Diffusion de sphères dures dans la droite réelle : comportement macroscopique et équilibre local
Diffusion processes and second order elliptic operators with singular coefficients for lower order terms.
Diffusion with an reflecting and absorbing level set boundary - a simulation study
Dirichlet functions of reflected Brownian motion
We give a complete analytical characterization of the functions transforming reflected Brownian motions to local Dirichlet processes.
Dirichlet problem for parabolic equations on Hilbert spaces
We study a linear second order parabolic equation in an open subset of a separable Hilbert space, with the Dirichlet boundary condition. We prove that a probabilistic formula, analogous to one obtained in the finite-dimensional case, gives a solution to this equation. We also give a uniqueness result.
Discrete approximations of generalized RBSDE with random terminal time
The convergence of discrete approximations of generalized reflected backward stochastic differential equations with random terminal time in a general convex domain is studied. Applications to investigation obstacle elliptic problem with Neumann boundary condition for partial differential equations are given.
Discrete Approximations of Strong Solutions of Reflecting SDEs with Discontinuous Coefficients
We study convergence for the Euler scheme for stochastic differential equations reflecting on the boundary of a general convex domain D ⊆ ℝd. We assume that the equation has the pathwise uniqueness property and its coefficients are measurable and continuous almost everywhere with respect to the Lebesgue measure. In the case D=[0,∞) new sufficient conditions ensuring pathwise uniqueness for equations with possibly discontinuous coefficients are given.
Discrétisation d'une équation différentielle stochastique et calcul approché d'espérances de fonctionnelles de la solution