Anticipative calculus for the Poisson process based on the Fock space
Anticipative calculus with respect to filtered Poisson processes
Appendice à l'exposé précédent : «Inégalités de semimartingales»
Approximation at first and second order of -order integrals of the fractional Brownian motion and of certain semimartingales.
Approximation par des intégrales de Stieltjes-Lebesgue d’intégrales stochastiques relatives au mouvement brownien indexé par
Approximation par des intégrales de Stieltjes-Lebesgue d’intégrales stochastiques relatives au mouvement brownien indexé par
Approximation theorems of Wong-Zakai type for stochastic differential equations in infinite dimensions [Book]
A.s. approximation results for multiplicative stochastic integrals
Asymptotic expansion of stochastic oscillatory integrals with rotation invariance
Asymptotics for the -deviation of the variance estimator under diffusion
We consider a diffusion process smoothed with (small) sampling parameter . As in Berzin, León and Ortega (2001), we consider a kernel estimate with window of a function of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the deviations such as
Asymptotics for the Lp-deviation of the variance estimator under diffusion
We consider a diffusion process Xt smoothed with (small) sampling parameter ε. As in Berzin, León and Ortega (2001), we consider a kernel estimate with window h(ε) of a function α of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the Lp deviations such as
Bilinear random integrals [Book]
Brownian excursions, stochastic integrals, and representation of Wiener functionals.
Brownian representations of cylindrical local martingales, martingale problem and strong Markov property of weak solutions of SPDEs in Banach spaces
The paper deals with three issues. First we show a sufficient condition for a cylindrical local martingale to be a stochastic integral with respect to a cylindrical Wiener process. Secondly, we state an infinite dimensional version of the martingale problem of Stroock and Varadhan, and finally we apply the results to show that a weak existence plus uniqueness in law for deterministic initial conditions for an abstract stochastic evolution equation in a Banach space implies the strong Markov property....
Calcul des variations sur un brownien subordonné
Calcul d'Ito sans probabilités
Calcul stochastique et inégalités de norme pour les martingales bi-browniennes. Application aux fonctions bi-harmoniques
On étend aux martingales bi-browniennes la formule de Itô et les inégalités de Burkholder-Gundy. On en déduit une démonstration probabiliste des inégalités de norme géométriques pour les fonctions bi-harmoniques sur le bi-disque.
Calcul stochastique non adapté par rapport à la mesure aléatoire de Poisson
Calcul stochastique pour les mesures signées
Cálculo diferencial estocástico para procesos con parámetro n-dimensional.
In this paper we obtain a representation of semimartingalas in the plane by means of stochastic integrals. Some applications to the study of random Markov gaussian fields are given.