Fonctionnelles browniennes généralisées intégrale de Feynman
Fonctions aléatoires gaussiennes, les résultats récents de M. Talagrand
Fonctions aléatoires lipschitziennes
Fonctions convexes et semimartingales dans une variété
Fonctions de corrélation des fonctions pseudo-aléatoires
Fonctions de Young et continuité des trajectoires d'une fonction aléatoire
À l’aide des notions de fonctions de Young et d’entropie métrique, nous donnons des conditions suffisantes d’existence d’une version à trajectoires continues et nous déterminons des modules de continuité uniforme pour les trajectoires de cette version dans des cas plus généraux que les fonctions aléatoires réelles gaussiennes.
Fonctions-spline et espérances conditionnelles de champs gaussiens
Formules de changement de variables
Formules de dualité sur l'espace de Poisson
Fourier Asymptotics of Statistically Self-Similar Measures.
Fourier multipliers for non-symmetric Lévy processes
We study Fourier multipliers resulting from martingale transforms of general Lévy processes.
Fractional Brownian motion and the Markov property.
Fractional brownian sheet.
Fractional Langevin equation with α-stable noise. A link to fractional ARIMA time series
We introduce a fractional Langevin equation with α-stable noise and show that its solution is the stationary α-stable Ornstein-Uhlenbeck-type process recently studied by Taqqu and Wolpert. We examine the asymptotic dependence structure of via the measure of its codependence r(θ₁,θ₂,t). We prove that is not a long-memory process in the sense of r(θ₁,θ₂,t). However, we find two natural continuous-time analogues of fractional ARIMA time series with long memory in the framework of the Langevin...
Fractional multiplicative processes
Statistically self-similar measures on [0, 1] are limit of multiplicative cascades of random weights distributed on the b-adic subintervals of [0, 1]. These weights are i.i.d., positive, and of expectation 1/b. We extend these cascades naturally by allowing the random weights to take negative values. This yields martingales taking values in the space of continuous functions on [0, 1]. Specifically, we consider for each H∈(0, 1) the martingale (Bn)n≥1 obtained when the weights take the values −b−H...
Fractional Ornstein-Uhlenbeck processes.
Fractional Poisson processes and related planar random motions.
Fragmentation of ordered partitions and intervals.
Frequent points for random walks in two dimensions.
From a kinetic equation to a diffusion under an anomalous scaling
A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process on , where is the two-dimensional torus. Here is an autonomous reversible jump process, with waiting times between two jumps with finite expectation value but infinite variance. is an additive functional of , defined as , where for small . We prove that the rescaled process converges in distribution to a two-dimensional Brownian motion. As a consequence, the appropriately...