Solutions of stochastic differential equations obeying the law of the iterated logarithm, with applications to financial markets.
Some results on convergence rates for probabilities of moderate deviations for sums of random variables.
Stability of precise Laplace's method under approximations; Applications
We study the fluctuations around non degenerate attractors of the empirical measure under mean field Gibbs measures. We prove that a mild change of the densities of these measures does not affect the central limit theorems. We apply this result to generalize the assumptions of [3] and [12] on the densities of the Gibbs measures to get precise Laplace estimates.
Stability of precise Laplace's method under approximations ; applications
Statistics of return times for weighted maps of the interval
Stochastic nonlinear Schrödinger equations driven by a fractional noise, well-posedness, large deviations and support.
Stone-Weierstrass type theorems for large deviations.
Subexponential tail asymptotics for a random walk with randomly placed one-way nodes
Sur la mécanique statistique d'une particule brownienne sur le tore
Sur l'équivalent du module de continuité des processus de diffusion
Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi
Sur les grandes déviations abstraites. Applications aux temps de séjours moyens d'un processus
Sur les grandes déviations en théorie de filtrage non linéaire
Soit la solution de l’équation différentielle stochastique suivante: , et considérons . L’objectif de cet article est d’établir le principe de grandes déviations pour la famille des lois induites par pour la norme höldérienne. Par conséquent, on montre le même résultat pour la famille des lois induites par . Enfin, on donne une application de ces résultats au filtrage non linéaire.
Tail behaviour of multiple random integrals and -statistics.
Tail probabilities of gaussian suprema and Laplace transform
The Aizenman-Sims-Starr and Guerra's schemes for the SK model with multidimensional spins.
The Berry-Esseen Bound for Minimum Contrast Estimators in the Independent not Identically Distributed Case.
The dynamics of mutation-selection algorithms with large population sizes
The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in
Considering the centered empirical distribution function Fn-F as a variable in , we derive non asymptotic upper bounds for the deviation of the -norms of Fn-F as well as central limit theorems for the empirical process indexed by the elements of generalized Sobolev balls. These results are valid for a large class of dependent sequences, including non-mixing processes and some dynamical systems.
The exit path of a Markov chain with rare transitions