An extension of the Clark-Ocone formula.
An extension of the Yamada-Watanabe condition for pathwise uniqueness to stochastic differential equations with jumps.
An extension theorem to rough paths
An integral representation for the Hellinger distance.
An introduction to probabilistic methods with applications
This special volume of the ESAIM Journal, Mathematical Modelling and Numerical Analysis, contains a collection of articles on probabilistic interpretations of some classes of nonlinear integro-differential equations. The selected contributions deal with a wide range of topics in applied probability theory and stochastic analysis, with applications in a variety of scientific disciplines, including physics, biology, fluid mechanics, molecular chemistry, financial mathematics and bayesian statistics....
An Itô type isometry for loops in via the brownian bridge
An operatorial approach to stochastic partial differential equations driven by linear multiplicative noise
An operator-valued stochastic integral, II
An operator-valued stochastic integral, III
An optimal Itô formula for Lévy processes.
An optimal quantitative two-scale expansion in stochastic homogenization of discrete elliptic equations
We establish an optimal, linear rate of convergence for the stochastic homogenization of discrete linear elliptic equations. We consider the model problem of independent and identically distributed coefficients on a discretized unit torus. We show that the difference between the solution to the random problem on the discretized torus and the first two terms of the two-scale asymptotic expansion has the same scaling as in the periodic case. In particular the L2-norm in probability of the H1-norm...
Analysis of the Rosenblatt process
We analyze the Rosenblatt process which is a selfsimilar process with stationary increments and which appears as limit in the so-called Non Central Limit Theorem (Dobrushin and Majòr (1979), Taqqu (1979)). This process is non-Gaussian and it lives in the second Wiener chaos. We give its representation as a Wiener-Itô multiple integral with respect to the Brownian motion on a finite interval and we develop a stochastic calculus with respect to it by using both pathwise type calculus and Malliavin...
Analytic and Geometric Logarithmic Sobolev Inequalities
We survey analytic and geometric proofs of classical logarithmic Sobolev inequalities for Gaussian and more general strictly log-concave probability measures. Developments of the last decade link the two approaches through heat kernel and Hamilton-Jacobi equations, inequalities in convex geometry and mass transportation.
Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula
Analytic stochastic processes
Analytical and numerical study of Kramers' exit problem. I.
Analytical and numerical study of Kramers' exit problem. II.
Analyticity of solutions and Kolmogorov's dissipation scale for 2D Navier-Stokes equations
Anticipation cancelled by a Girsanov transformation : a paradox on Wiener space
Anticipative calculus for the Poisson process based on the Fock space