Continuity Properties of the Extension of a Locally Lipschitz Continuous Map to the Space of Probability Measures.
Convergence faible et principe d'invariance pour des martingales à valeurs dans des espaces de Sobolev
Convergence of iterative algorithms to common random fixed points of random operators.
Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces
Cylindrical measures on tensor products of Banach spaces and random linear operators.
Dynamical systems with multiplicative perturbations
Eigenvalue curves of asymmetric tridiagonal random matrices.
Erratum to the paper "On the Kaczmarz algorithm of approximation in infinite-dimensional spaces" (Studia Math. 148 (2001), 75-86)
Estudio del carácter markoviano fuerte y regularidades de la solución de ecuaciones integrales estocásticas Ito generalizadas.
El objetivo de este trabajo es un estudio sobre los caracteres felleriano y markoviano fuerte y las propiedades de regularidad del proceso solución de una ecuación integral estocástica generalizada (tipo Ito), pero generalizada en el sentido de considerar una formulación en términos de procesos operador-valuados. Esta formulación generaliza simultánea e independientemente las integrales de Cabaña y Daletsky.
Étude des opérateurs de Schrödinger à potentiel aléatoire en dimension 1
Exponential decay of averaged Green functions for random Schrödinger operators. A direct approach
Extension of the method of quasilinearization for stochastic initial value problems.
Factorisation d'opérateurs aléatoires, d'après Benyamini et Gordon
Fredholm random operators and random subspaces in Banach spaces
From power pure point to continuous spectrum in disordered systems
Functional integro-differential stochastic evolution equations in Hilbert space.
Gaussian random band matrices and operator-valued free probability theory
Global asymptotic stability of solutions of cubic stochastic difference equations.
Global Poissonian behavior of the eigenvalues and localization centers of random operators in the localized phase
In the present note, we review some recent results on the spectral statistics of random operators in the localized phase obtained in [12]. For a general class of random operators, we show that the family of the unfolded eigenvalues in the localization region considered jointly with the associated localization centers is asymptotically ergodic. This can be considered as a generalization of [10]. The benefit of the present approach is that one can vary the scaling of the unfolded eigenvalues covariantly...
Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients⋆⋆⋆
In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence of polynomial subspaces that features better convergence properties compared to standard polynomial subspaces such as Total Degree or Tensor Product. We consider then the Stochastic Collocation method, and use the previous estimates to introduce...