Temps locaux et intégration stochastique pour les processus de Dirichlet
The Banach space of workable contingent claims in arbitrage theory
The central limit theorem for stochastic integrals.
The change of variables formula on Wiener space
The fBm Itô's formula through analytic continuation.
The gauge and conditional gauge theorem
The Kurzweil-Henstock theory of stochastic integration
The Kurzweil-Henstock approach has been successful in giving an alternative definition to the classical Itô integral, and a simpler and more direct proof of the Itô Formula. The main advantage of this approach lies in its explicitness in defining the integral, thereby reducing the technicalities of the classical stochastic calculus. In this note, we give a unified theory of stochastic integration using the Kurzweil-Henstock approach, using the more general martingale as the integrator. We derive...
The multiple stochastic integrals and “non-Poissonian” transformations of the gamma measure.
The representation of Poisson functionals
The total continuity of natural filtrations
Théorème des résidus asymptotique pour le mouvement brownien sur une surface riemannienne compacte
Théorèmes limite fonctionnels pour les processus de vraisemblance (cadre asymptotiquement non gaussien)
Transformations of index set for Skorokhod integral with respect to Gaussian processes.
Trees and asymptotic expansions for fractional stochastic differential equations
In this article, we consider an n-dimensional stochastic differential equation driven by a fractional brownian motion with Hurst parameter H>1/3. We derive an expansion for E[f(Xt)] in terms of t, where X denotes the solution to the SDE and f:ℝn→ℝ is a regular function. Comparing to F. Baudoin and L. Coutin, Stochastic Process. Appl.117 (2007) 550–574, where the same problem is studied, we provide an improvement in three different directions: we are able to consider equations with drift,...
Tribus de Meyer et théorie des processus
Two results on continuity and boundedness of stochastic convolutions