-norm of infinitely divisible random vectors and certain stochastic integrals.
-estimates for SPDE with discontinuous coefficients in domains.
solutions of BSDEs with stochastic Lipschitz condition.
-uniqueness for infinite dimensional symmetric Kolmogorov operators : the case of variable diffusion coefficients
La classe des semimartingales qui permettent d'intégrer les processus optionnels
La convergence de la série de Picard pour les EDS
La formule d'Ito pour le mouvement brownien, d'après G. Brosamler
LAMN property for hidden processes : the case of integrated diffusions
In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process X. Our data are given by ∫01X(s+i)/n dμ(s) for i=0, …, n−1 and the unknown parameter appears in the diffusion coefficient of the process X only. Although the data are neither markovian nor gaussian we can write down, with help of Malliavin calculus, an explicit expression for the log-likelihood of the model, and then study the asymptotic...
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