Set-valued Stratonovich integral
The purpose of the paper is to introduce a set-valued Stratonovich integral driven by a one-dimensional Brownian motion. We discuss the existence of this integral and investigate its properties.
Sharp estimates for the convergence of the density of the Euler scheme in small time.
Sharp maximal inequality for martingales and stochastic integrals.
Sharp norm inequality for bounded submartingales and stochastic integrals.
Simplified Malliavin calculus
Simulation and approximation of Lévy-driven stochastic differential equations
We consider the approximate Euler scheme for Lévy-driven stochastic differential equations. We study the rate of convergence in law of the paths. We show that when approximating the small jumps by Gaussian variables, the convergence is much faster than when simply neglecting them. For example, when the Lévy measure of the driving process behaves like |z|−1−αdz near 0, for some α ∈ (1,2), we obtain an error of order 1/√n with a computational cost of order nα. For a similar error when neglecting the...
Simulation and approximation of Lévy-driven stochastic differential equations
We consider the approximate Euler scheme for Lévy-driven stochastic differential equations. We study the rate of convergence in law of the paths. We show that when approximating the small jumps by Gaussian variables, the convergence is much faster than when simply neglecting them. For example, when the Lévy measure of the driving process behaves like |z|−1−αdz near 0, for some α∈ (1,2), we obtain an error of order 1/√n with a computational cost of order nα. For a similar error when neglecting the...
Singularité du spectre de l'opérateur de Schrödinger aléatoire dans un ruban ou un demi-ruban
Singularity functions for fractional processes : application to the fractional brownian sheet
Skew products, regular conditional probabilities and stochastic differential equations : a technical remark
Skorokhod imbedding via stochastic integrals
Small and big probability worlds
Small random perturbations of infinite dimensional dynamical systems and nucleation theory
Small time asymptotics of Ornstein-Uhlenbeck densities in Hilbert spaces.
Smooth measures, the Malliavin calculus and approximations in infinitedimensional spaces
Smoothness of the law of some one-dimensional jumping S.D.E.s with non-constant rate of jump.
Smoothness of the law of the supremum of the fractional Brownian motion.
Sobolev solution for semilinear PDE with obstacle under monotonicity condition.
Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise.
Solution explicite de l’équation