The principle of truncations in applied probability
The probabilistic approach to the analysis of the limiting behavior of an integro-differential equation depending on a small parameter, and its application to stochastic processes.
The realization of positive random variables via absolutely continuous transformations of measure on Wiener space.
The representation of Poisson functionals
The right tail exponent of the Tracy–Widom distribution
The Tracy–Widom distribution is the large dimensional limit of the top eigenvalue of random matrix ensembles. We use the stochastic Airy operator representation to show that as the tail of the Tracy–Widom distribution satisfies
The set of probability distribution solutions of a linear functional equation
Let (Ω,,P) be a probability space and let τ: ℝ×Ω → ℝ be a function which is strictly increasing and continuous with respect to the first variable, measurable with respect to the second variable. Given the set of all continuous probability distribution solutions of the equation we determine the set of all its probability distribution solutions.
The smallest g-supermartingale and reflected BSDE with single and double obstacles
The statistical equilibrium of an isotropic stochastic flow with negative Lyapounov exponents is trivial
The steepest descent method for forward-backward SDEs.
The stochastic logistic equation : stationary solutions and their stability
The Study of two Evolutionary random Nonlinear Problems
The total continuity of natural filtrations
The value function in ergodic control of diffusion processes with partial observations II
The problem of minimizing the ergodic or time-averaged cost for a controlled diffusion with partial observations can be recast as an equivalent control problem for the associated nonlinear filter. In analogy with the completely observed case, one may seek the value function for this problem as the vanishing discount limit of value functions for the associated discounted cost problems. This passage is justified here for the scalar case under a stability hypothesis, leading in particular to a "martingale"...
The wave equation in random domains : localization of the normal modes in the small frequency region
The Yamada-Watanabe-Engelbert theorem for general stochastic equations and inequalities.
Théorème des résidus asymptotique pour le mouvement brownien sur une surface riemannienne compacte
Théorème du support pour les diffusions réfléchies de type Ventcell
Théorèmes limite fonctionnels pour les processus de vraisemblance (cadre asymptotiquement non gaussien)
Theoretical and numerical aspects of stochastic nonlinear Schrödinger equations
We describe several results obtained recently on stochastic nonlinear Schrödinger equations. We show that under suitable smoothness assumptions on the noise, the nonlinear Schrödinger perturbed by an additive or multiplicative noise is well posed under similar assumptions on the nonlinear term as in the deterministic theory. Then, we restrict our attention to the case of a focusing nonlinearity with critical or supercritical exponent. If the noise is additive, smooth in space and non degenerate,...
Three examples of brownian flows on
We show that the only flow solving the stochastic differential equation (SDE) on