A clark-ocone formula in UMD Banach spaces.
A conservative evolution of the Brownian excursion.
A criterium for the strict positivity of the density of the law of a Poisson process.
A generalization of the conservation integral
Starting from the scheme given by Hudson and Parthasarathy [7,11] we extend the conservation integral to the case where the underlying operator does not commute with the time observable. It turns out that there exist two extensions, a left and a right conservation integral. Moreover, Itô's formula demands for a third integral with two integrators. Only the left integral shows similar continuity properties to that derived in [11] used for extending the integral to more than simple integrands. In...
A hull and white formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility.
A Malliavin calculus method to study densities of additive functionals of SDE’s with irregular drifts
We present a general method which allows to use Malliavin Calculus for additive functionals of stochastic equations with irregular drift. This method uses the Girsanov theorem combined with Itô–Taylor expansion in order to obtain regularity properties for this density. We apply the methodology to the case of the Lebesgue integral of a diffusion with bounded and measurable drift.
A Milstein-type scheme without Lévy area terms for SDEs driven by fractional brownian motion
In this article, we study the numerical approximation of stochastic differential equations driven by a multidimensional fractional Brownian motion (fBm) with Hurst parameter greater than 1/3. We introduce an implementable scheme for these equations, which is based on a second-order Taylor expansion, where the usual Lévy area terms are replaced by products of increments of the driving fBm. The convergence of our scheme is shown by means of a combination of rough paths techniques and error bounds...
A stochastic control problem.
A type of Gauss' divergence formula on Wiener spaces.
Analysis of the Rosenblatt process
We analyze the Rosenblatt process which is a selfsimilar process with stationary increments and which appears as limit in the so-called Non Central Limit Theorem (Dobrushin and Majòr (1979), Taqqu (1979)). This process is non-Gaussian and it lives in the second Wiener chaos. We give its representation as a Wiener-Itô multiple integral with respect to the Brownian motion on a finite interval and we develop a stochastic calculus with respect to it by using both pathwise type calculus and Malliavin...
Anticipative calculus with respect to filtered Poisson processes
Anticipative direct transformations on the Poisson space
Asymptotic behavior of weighted quadratic variation of bi-fractional Brownian motion
We prove, by means of Malliavin calculus, the convergence in of some properly renormalized weighted quadratic variations of bi-fractional Brownian motion (biFBM) with parameters and , when and .
Besov regularity for the generalized local time of the indefinite Skorohod integral
Brownian motion with respect to time-changing riemannian metrics, applications to Ricci flow
We generalize brownian motion on a riemannian manifold to the case of a family of metrics which depends on time. Such questions are natural for equations like the heat equation with respect to time dependent laplacians (inhomogeneous diffusions). In this paper we are in particular interested in the Ricci flow which provides an intrinsic family of time dependent metrics. We give a notion of parallel transport along this brownian motion, and establish a generalization of the Dohrn–Guerra or damped...
Calcul de Malliavin et probabilité invariante d'une chaîne de Markov
Calcul de Malliavin et régularité de la densité d'une probabilité invariante d'une chaîne de Markov
Calcul stochastique non adapté par rapport à la mesure aléatoire de Poisson
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...
Clark–Ocone formulas and Poincaré inequalities on the discrete cube