L'approximation u.c.p. et la continuité de certaines intégrales stochastiques dépendant d'un paramètre
Large deviation principle and inviscid shell models.
Large deviation principle for a stochastic heat equation with spatially correlated noise.
Large deviation principle for enhanced gaussian processes
Large deviations and support results for nonlinear Schrödinger equations with additive noise and applications
Sample path large deviations for the laws of the solutions of stochastic nonlinear Schrödinger equations when the noise converges to zero are presented. The noise is a complex additive gaussian noise. It is white in time and colored in space. The solutions may be global or blow-up in finite time, the two cases are distinguished. The results are stated in trajectory spaces endowed with topologies analogue to projective limit topologies. In this setting, the support of the law of the solution is also...
Large deviations and support results for nonlinear Schrödinger equations with additive noise and applications
Sample path large deviations for the laws of the solutions of stochastic nonlinear Schrödinger equations when the noise converges to zero are presented. The noise is a complex additive Gaussian noise. It is white in time and colored in space. The solutions may be global or blow-up in finite time, the two cases are distinguished. The results are stated in trajectory spaces endowed with topologies analogue to projective limit topologies. In this setting, the support of the law of the solution is...
Large deviations for invariant measures of stochastic reaction–diffusion systems with multiplicative noise and non-Lipschitz reaction term
Large deviations for one dimensional diffusions with a strong drift.
Large deviations for some Poisson random integrals
Large population limit and time behaviour of a stochastic particle model describing an age-structured population
We study a continuous-time discrete population structured by a vector of ages. Individuals reproduce asexually, age and die. The death rate takes interactions into account. Adapting the approach of Fournier and Méléard, we show that in a large population limit, the microscopic process converges to the measure-valued solution of an equation that generalizes the McKendrick-Von Foerster and Gurtin-McCamy PDEs in demography. The large deviations associated with this convergence are studied. The upper-bound...
Law equivalence of solutions of some linear stochastic equations in Hilbert spaces
Sufficient and necessary conditions for equivalence of the distributions of the solutions of some linear stochastic equations in Hilbert spaces are given. Some facts in the theory of perturbations of semigroup generators and Zabczyk's results on law equivalence are used.
Les filtrations de certaines martingales du mouvement brownien dans
Les intervalles de constance de
Les -topologies en théorie du potentiel
La topologie fine a été introduite pour fournir un cadre intrinsèque à la théorie du potentiel. Cependant les ouverts fins ne possèdent pas certaines propriétés dont celle de Lindeberg. Cette considération nous conduit à introduire des topologies moins finies appelées -topologies ). Nous démontrons pour ces -topologies un critère analogue à celui établi par N. Wiener, pour les ouverts fins. Puis nous nous intéressons à la théorie des équations différentielles stochastiques sur les -ouverts.
Les processus à accroissements indépendants et les équations de structure
Les semi-martingales formelles
Les systèmes-produits et l'espace de Fock, d'après W. Arveson
Level crossings and turning points of random hyperbolic polynomials.
Lévy's area under conditioning
Liens entre équations différentielles stochastiques et ordinaires