# A Course on Rough Paths: With an Introduction to Regularity Structures

@inproceedings{Friz2014ACO, title={A Course on Rough Paths: With an Introduction to Regularity Structures}, author={Peter K. Friz and Martin Hairer}, year={2014} }

Introduction.- The space of rough paths.- Brownian motion as a rough path.- Integration against rough paths.- Stochastic integration and Ito's formula.- Doob-Meyer type decomposition for rough paths.- Operations on controlled rough paths.- Solutions to rough differential equations.- Stochastic differential equations.- Gaussian rough paths.- Cameron-Martin regularity and applications.- Stochastic partial differential equations.- Introduction to regularity structures.- Operations on modelled…

## 237 Citations

Pathwise It\^o Calculus for Rough Paths and Rough PDEs with Path Dependent Coefficients

- Computer Science, Mathematics
- 2014

Rough path theory and stochastic calculus

- MathematicsSugaku Expositions
- 2019

T. Lyons' rough path theory is something like a deterministic version of K. Ito's theory of stochastic differential equations, combined with ideas from K. T. Chen's theory of iterated path integrals.…

Density Bounds for Solutions to Differential Equations Driven by Gaussian Rough Paths

- Mathematics, Computer Science
- 2017

Using Malliavin calculus, rough paths techniques and interpolation inequalities, upper bounds are established on the density of the corresponding solution for any fixed time $$t>0$$ t > 0 .

Averaging principle for fast-slow system driven by mixed fractional Brownian rough path

- Mathematics
- 2020

Precise local estimates for differential equations driven by fractional Brownian motion: Hypoelliptic case

- MathematicsThe Annals of Probability
- 2022

This article is concerned with stochastic differential equations driven by a $d$ dimensional fractional Brownian motion with Hurst parameter $H>1/4$, understood in the rough paths sense. Whenever the…

Ito formulae for the stochastic heat equation via the theories of rough paths and regularity structures

- Mathematics
- 2019

In this thesis, we develop a general theory to prove the existence of several Ito formulae on the one-dimensional stochastic heat equation driven by additive space-time white noise. That is denoting…

Flows driven by rough paths

- Mathematics
- 2012

We devise in this work a simple mechanism for constructing flows on a Banach space from approximate flows, and show how it can be used in a simple way to reprove from scratch and extend the main…

A Transfer Principle for Branched Rough Paths

- Mathematics
- 2022

A branched rough path X consists of a rough integral calculus for X : [0 , T ] → R d which may fail to satisfy integration by parts. Using Kelly’s bracket extension [Kel12Kel12], we define a notion…

## References

Introduction to KPZ

- Mathematics
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This is an introductory survey of the Kardar-Parisi-Zhang equation (KPZ). The first chapter provides a non-rigorous background to the equation and to some of the many models which are supposed to lie…