Monsieur Pierre-Yves Hénin, Président de l'Université Paris 1, acceuille des participants à la conférence et se félicite que le Centre Pierre Mendès-France serve de cadre à cette manifestation scientifique. Bande son disponible au format mp3 Durée : 6 mn

Monsieur Cuong Le Van, Directeur du Centre d'Economie de la Sorbonne, présente ce centre en décrivant plus particulièrement les thématiques de recherche en mathématiques qui y sont développées. Bande son disponible au format mp3 Durée : 4 mn

Consider the stochastic wave equation in dimension , , where denotes the formal derivative of a Gaussian stationary random field, white in time and correlated in space. Using Malliavin calculus, with Quer-Sardanyons we proved the existence and regularity of density of the law of the solution to the SPDE for any fixed . Denote this density by . More recently, with R. Dalang, we have established joint Hölder continuity in of...

Marta SANZ-SOLE. Universitat de Barcelona. Bande son disponible au format mp3 Durée : 4 mn

The long term behaviour of dissipatively synchronized deterministic systems is determined by the system with the averaged vector field of the original uncoupled systems. This effect is preserved in the presence of environmental i.e., background or additive noise provided stochastic stationary solutions are used instead of steady state solutions. Random dynamical systems and random attractors provide the appropriate mathematical framework for such problems and require Ito...

Peter KLOEDEN. Johann Wolfgang Goethe University. Bande son disponible au format mp3 Durée : 4 mn

We want to present some results on gradient systems with convex potential in finite and infinite dimension. The techniques are based on recent developments in the theory of gradient flows in the Wasserstein metric. (joint work with L. Ambrosio & G. Savaré). Lorenzo ZAMBOTTI. Université Paris 6. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1182789954236 (pdf) Bande son disponible au format...

Lorenzo ZAMBOTTI. Université Paris 6. Bande son disponible au format mp3 Durée : 4 mn

As a model for multiscale systems under random influences on physical boundary, a stochastic partial differential equation under a fast random dynamical boundary condition is investigated. An effective equation is derived and justified by reducing the random dynamical boundary condition to a usual random boundary condition. The effective system is still a stochastic partial differential equation, but is more tractable. Furthermore, the quantitative comparison between the solution of the...

Jinqiao DUAN. Illinois Institute of Technology. Bande son disponible au format mp3 Durée : 4 mn

We consider a directed polymer on the unit circle, with a continuous direction (time) parameter , defined as a simple random walk subjected via a Gibbs measure to a Hamiltonian whose increments in time have either long memory () or semi-long memory (), and which also depends on a space parameter (position/state of the polymer). is interpreted as the Hurst parameter of an infinite-dimensional fractional Brownian motion. The partition function of this polymer is linked to stochastic PDEs via...

Frederi VIENS. Purdue University. Bande son disponible au format mp3 Durée : 4 mn

In this talk we consider the stochastic heat equation in , with vanishing initial conditions, driven by a Gaussian noise which is fractional in time, with Hurst index , and colored in space, with spatial covariance given by a function . Our main result gives the necessary and sufficient condition on for the existence of the process solution. When is the Riesz kernel of order this condition is , which is a relaxation of the condition encountered when the noise is white in space....

Raluca BALAN. University of Ottawa. Bande son disponible au format mp3 Durée : 7 mn

In the first part of the talk, we will study the convergence of some weighted power variations of a fractional Brownian motion B. In the second part, we will apply the results obtained in the first part to compute the exact rate of convergence of some approximating schemes associated to scalar stochastic differential equations driven by B. In particular, we will be able to compute explicitly the limit of the error between the exact solution and the considered scheme. Ivan NOURDIN. Université...

Ivan NOURDIN. Université Paris 6. Bande son disponible au format mp3 Durée : 4 mn

This talk does not suppose a priori that the evolution of a financial asset price is a semimartingale. The stochastic integral intervening in the definition of self-financing property is forward integral. If one requires that a certain minimal class of investor strategies are self-financing, previous prices are forced to be finite quadratic variation processes. The non-arbitrage property is not excluded if the class of admissible strategies is restricted. The classical notion of martingale...

Francesco RUSSO. Université Paris 13. Bande son disponible au format mp3 Durée : 4 mn

In this talk, we will describe some recent results concerning stochastic differential equations driven by a multidimensional fractional Brownian motion with Hurst parameter 1/3H1/2. Some simplifications in the rough path analysis have allowed us to study some properties of the processes associated to this kind of equation, and we will try to give an overview on three of them: an asymptotic expansion for the law of the process, a weak approximation type result, and an existence and uniqueness...

Samy TINDEL. Université de Nancy. Bande son disponible au format mp3 Durée : 3 mn

In this work, we consider the Korteweg- de Vries equation perturbed by a random force of white noise type, additive or multiplicative. In a series of work, in collaboration with Y. Tsutsumi, we have studied existence and uniqueness in the additive case for very irregular noises. These use the functional framework introduced by J. Bourgain. We use similar tools to prove existence and uniqueness for a multiplicative noise. We are not able to consider irregular noises and have to assume...

Arnaud DEBUSSCHE. ENS Cachan. Bande son disponible au format mp3 Durée : 2 mn

We study from a mathematical point of view a model equation for Bose Einstein condensation, in the case where the trapping potential varies randomly in time. The model is a nonlinear Schrödinger equation, with a quadratic potential with white noise fluctuations in time. We prove the existence of strong solutions in 1D and 2D in the energy space. The blow-up phenomenon will also be discussed under critical and super critical nonlinear interactions in the attractive case. This is a joint work...

We prove that an averaging principle holds for a general class of stochastic reaction-diffusion systems, having unbounded multiplicative noise, in any space dimension. We show that the classical Khasminskii approach for systems with a finite number of degrees of freedom can be extended to infinite dimensional systems. Sandra CERRAI. Universita di Firenze. Document associé : support de présentation :...

Sandra CERRAI. Universita di Firenze. Bande son disponible au format mp3 Durée : 6 mn