We derive a change of variable formula for non-anticipative functionals defined on the space of Rd -valued right-continuous paths with left limits. The functionals are only required to possess… (More)

We prove that the Cauchy problem for the three-dimensional Navier–Stokes equations is ill-posed in Ḃ −1,∞ ∞ in the sense that a “norm inflation” happens in finite time. More precisely, we show that… (More)

Given an n-dimensional compact manifold M , endowed with a family of Riemannian metrics g(t), a Brownian motion depending on the deformation of the manifold (via the family g(t) of metrics) is… (More)

Motivated by financial applications, we study convex analysis for modules over the ordered ring L0 of random variables. We establish a module analogue of locally convex vector spaces, namely locally… (More)

A one-step scheme is constructed, which, as the Milstein scheme, has the strong approximation property of order 1; in contrast to the Milstein scheme, our scheme does not involve the simulation of… (More)

Abstract: Extensions of the Nourdin-Peccati analysis to R-valued random variables are obtained by taking conditional expectation on the Wiener space. Several proof techniques are explored, from… (More)

In this paper we prove a large deviations principle for the invariant measures of a class of reaction–diffusion systems in bounded domains of Rd , d 1, perturbed by a noise of multiplicative type. We… (More)

The principal part of the error in the Euler scheme for an SDE with smooth coefficients can be expressed as a generalized Watanabe distribution on Wiener space. To cite this article: P. Malliavin, A.… (More)

This work establishes and exploits a connection between the invariant measure of stochastic partial differential equations (SPDEs) and the law of bridge processes. Namely, it is shown that the… (More)