Calculs formels sur les e.d.s. de Stratonovitch
Capacités gaussiennes
On étudie les espaces de Sobolev construits sur un espace localement convexe muni d’une mesure gaussienne centree . Si est de Radon, on démontre que les capacités naturelles sont tendues sur les compacts. Cela résulte d’un principe général relatif aux quasi-normes.On s’intéresse également aux fonctions quasi-continues a valeurs banachiques, ce qui est utile pour les propriétés de Nikodym, et à des applications à la continuité des trajectoires des intégrales stochastiques.
Caractérisation des martingales à deux paramètres indépendantes du chemin
Caractérisation des semimartingales
Carthaginian enlargement of filtrations
This work is concerned with the theory of initial and progressive enlargements of a reference filtration F with a random timeτ. We provide, under an equivalence assumption, slightly stronger than the absolute continuity assumption of Jacod, alternative proofs to results concerning canonical decomposition of an F -martingale in the enlarged filtrations. Also, we address martingales’ characterization in the enlarged filtrations in terms of martingales in the reference filtration, as well as predictable...
Central and non-central limit theorems for weighted power variations of fractional brownian motion
In this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order q≥2 of the fractional brownian motion with Hurst parameter H∈(0, 1), where q is an integer. The central limit holds for 1/2q<H≤1−1/2q, the limit being a conditionally gaussian distribution. If H<1/2q we show the convergence in L2 to a limit which only depends on the fractional brownian motion, and if H>1−1/2q we show the convergence in L2 to a stochastic integral...
Chain rules and p-variation
The main result is a Young-Stieltjes integral representation of the composition ϕ ∘ f of two functions f and ϕ such that for some α ∈ (0,1], ϕ has a derivative satisfying a Lipschitz condition of order α, and f has bounded p-variation for some p < 1 + α. If given α ∈ (0,1], the p-variation of f is bounded for some p < 2 + α, and ϕ has a second derivative satisfying a Lipschitz condition of order α, then a similar result holds with the Young-Stieltjes integral replaced by its extension.
Changements de temps et intégrales stochastiques
Changing time for two-parameter strong martingales
Chaos de Wiener et intégrale de Feynman
Chaos expansions and local times.
In this note we prove that the Local Time at zero for a multiparametric Wiener process belongs to the Sobolev space Dk - 1/2 - ε,2 for any ε > 0. We do this computing its Wiener chaos expansion. We see also that this expansion converges almost surely. Finally, using the same technique we prove similar results for a renormalized Local Time for the autointersections of a planar Brownian motion.
Characterization of a regular family of semimartingales by line integrals.
Closedness of some spaces of stochastic integrals
Cohomologie de Bismut-Nualart-Pardoux et cohomologie de Hochschild entière
Compensation de processus à variation finie non localement intégrables
Compensation multiplicative et «produits de Wick»
Completion measurable linear functionals on a probability space
Composition of independent stochastic variables
Conformal martingales and analytic functions.
Construction of semimartingales from pieces by the method of excursion point processes