We introduce a new notion of “regularity structure” that provides an algebraic framework
allowing to describe functions and/or distributions via a kind of “jet” or local Taylor expansion …

A new volume of philosophical essays by Bernard Williams. The book is a successor to
Problems of the Self, but whereas that volume dealt mainly with questions of personal …

We give a systematic description of a canonical renormalisation procedure of stochastic
PDEs containing nonlinearities involving generalised functions. This theory is based on the …

The main objective of this book is to give an overview of the theory of Hamilton–Jacobi–
Bellman (HJB) partial differential equations (PDEs) in infinite-dimensional Hilbert spaces …

We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional
cubic wave equation, which is also known as the hyperbolic Φ 3 4-model. This result is the …

Second order linear parabolic and elliptic equations arise frequently in mathematics and
other disciplines. For example parabolic equations are to be found in statistical mechanics …

Stochastic partial differential equations are ubiquitous in mathematical modeling. Yet, many
such equations are too singular to admit classical treatment. In this article we review some …

STRONG SOLUTIONS TO THE STOCHASTIC QUANTIZATION EQUATIONS Scuola Normale
Superiore di Pisa and Ecole Normale Supérieure de Cach Page 1 The Annals of Probability …

This book is dedicated to the mathematical study of two-dimensional statistical
hydrodynamics and turbulence, described by the 2D Navier–Stokes system with a random …

This volume deals with the random perturbation of PDEs which lack well-posedness, mainly
because of their non-uniqueness, in some cases because of blow-up. The aim is to show …