Peter K. Friz Martin Hairer With an Introduction to Regularity Structures Second Edition
Page 1 Universitext Peter K. Friz Martin Hairer A Course on Rough Paths With an …

We introduce an approach to study certain singular partial differential equations (PDEs)
which is based on techniques from paradifferential calculus and on ideas from the theory of …

We introduce a new concept of solution to the KPZ equation which is shown to extend the
classical Cole-Hopf solution. This notion provides a factorisation of the Cole-Hopf solution …

Dynamical heterogeneities in a colloidal fluid close to gelation are studied by means of
computer simulations. A clear distinction between some fast particles and the rest, slow …

We build a hybrid theory of rough stochastic analysis which seamlessly combines the
advantages of both It\^ o's stochastic and Lyons' rough differential equations. This gives a …

We construct a pathwise integration theory, associated with a change of variable formula, for
smooth functionals of continuous paths with arbitrary regularity defined in terms of the notion …

In this article, we show how the theory of rough paths can be used to provide a notion of
solution to a class of nonlinear stochastic PDEs of Burgers type that exhibit too‐high spatial …

We introduce a general weak formulation for PDEs driven by rough paths, as well as a new
strategy to prove well-posedness. Our procedure is based on a combination of fundamental …

This article is devoted to define and solve an evolution equation of the form dy t= Δ yt dt+ dX
t (yt), where Δ stands for the Laplace operator on a space of the form L^ p (\mathbb R^ n) …

In recent works, beginning with [76], several stochastic geophysical fluid dynamics (SGFD)
models have been derived from variational principles. In this paper, we introduce a new …