De Finetti's-type results for some families of non identically distributed random variables.
Decay of correlations for non Hölderian dynamics. A coupling approach.
Decomposability of Cylindrical Martingales and Absolutely Summing Operators.
Décomposition atomique de martingales de la classe
Décomposition de Kunita-Watanabe
Décomposition des martingales locales et raréfaction des sauts
Décomposition des processus aléatoires, une comparaison entre les méthodes factorielles et l'analyse spectrale
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.
Décompositions multiplicatives de semimartingales exponentielles et applications
Defaultable bonds with an infinite number of Lévy factors
A market with defaultable bonds where the bond dynamics is in a Heath-Jarrow-Morton setting and the forward rates are driven by an infinite number of Lévy factors is considered. The setting includes rating migrations driven by a Markov chain. All basic types of recovery are investigated. We formulate necessary and sufficient conditions (generalized HJM conditions) under which the market is arbitrage-free. Connections with consistency conditions are discussed.
Degenerate limit laws for the maxima of trigonometric polynomials with random coefficients
Degree distribution nearby the origin of a preferential attachment graph.
Delay equations driven by rough paths.
Demiconvergence of processes indexed by two indices
Démonstration «atomique» des inégalités de Burkholder-Davis-Gundy
Démonstration d'un théorème de F. Knight à l'aide de martingales exponentielles
Démonstration élémentaire d'un résultat d'Azéma et Jeulin
Démonstration simple d'un résultat sur le temps local
Density estimation for one-dimensional dynamical systems
In this paper we prove a Central Limit Theorem for standard kernel estimates of the invariant density of one-dimensional dynamical systems. The two main steps of the proof of this theorem are the following: the study of rate of convergence for the variance of the estimator and a variation on the Lindeberg–Rio method. We also give an extension in the case of weakly dependent sequences in a sense introduced by Doukhan and Louhichi.
Density Estimation for One-Dimensional Dynamical Systems
In this paper we prove a Central Limit Theorem for standard kernel estimates of the invariant density of one-dimensional dynamical systems. The two main steps of the proof of this theorem are the following: the study of rate of convergence for the variance of the estimator and a variation on the Lindeberg–Rio method. We also give an extension in the case of weakly dependent sequences in a sense introduced by Doukhan and Louhichi.