Stochastic integral representation of the modulus of Brownian local time and a central limit theorem.
Smoothness of the law of the supremum of the fractional Brownian motion.
Points of positive density for smooth functionals.
Regularity of the density for the stochastic heat equation.
Application du calcul de Malliavin aux équations différentielles stochastiques sur le plan
Une remarque sur le développement en chaos d'une diffusion
Différents types de martingales à deux indices
Une formule d'Itô pour les martingales continues à deux indices et quelques applications
Caracterización geométrica de la independencia en un espacio gaussiano.
Stochastic calculus with respect to fractional Brownian motion
Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter called the Hurst index. In this conference we will survey some recent advances in the stochastic calculus with respect to fBm. In the particular case , the process is an ordinary Brownian motion, but otherwise it is not a semimartingale and Itô calculus cannot be used. Different approaches have been introduced to construct stochastic integrals with respect to fBm:...
Contribución al estudio de la integral estocástica.
Decomposition of two parameter martingales.
In this paper we exhibit some decompositions in orthogonal stochastic integrals of two-parameter square integrable martingales adapted to a Brownian sheet which generalize the representation theorem of E. Wong and M. Zakai ([6]). Concretely, a development in a series of multiple stochastic integrals is obtained for such martingales. These results are applied for the characterization of martingales of path independent variation.
The partial Malliavin calculus
Anticipative calculus for the Poisson process based on the Fock space
Stochastic integral of divergence type with respect to fractional brownian motion with Hurst parameter
Régularité des noyaux de Wiener d’une diffusion
Caractérisation des martingales à deux paramètres indépendantes du chemin
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 D 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.
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.
Onsager-Machlup functionals for solutions of stochastic boundary-value problems
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