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 …

In data science, one is often confronted with a time series representing measurements of
some quantity of interest. Usually, in a first step, features of the time series need to be …

We construct an explicit transitive free action of a Banach space of Hölder functions on the
space of branched rough paths, which yields in particular a bijection between these two …

We introduce the class of “smooth rough paths” and study their main properties. Working in a
smooth setting allows us to discard sewing arguments and focus on algebraic and geometric …

The signature of a path can be described as its full non-commutative exponential. Following
T. Lyons, we regard its expectation, the expected signature, as a path space analogue of the …

We exhibit an explicit natural isomorphism between spaces of branched and geometric
rough paths. This provides a multi-level generalisation of the isomorphism of Lejay–Victoir …

In this paper, we show how one can view certain models in regularity structures as some
form of geometric rough paths. This is performed by identifying the deformed Butcher …

Abstract The Hairer–Kelly map has been introduced for establishing a correspondence
between geometric and non-geometric rough paths. Recently, a new renormalisation on …

Using some basic notions from the theory of Hopf algebras and quasi-shuffle algebras, we
introduce rigorously a new family of rough paths: the quasi-geometric rough paths. We …

In this work, we provide a combinatorial formalism for dealing with the cancellations that
have appeared recently in the context of dispersive PDEs with random initial data. The main …