# A Course on Rough Paths

@inproceedings{Friz2014ACO, title={A Course on Rough Paths}, author={Peter K. Friz and Martin Hairer}, year={2014} }

We give a short overview of the scopes of both the theory of rough paths and the theory of regularity structures. The main ideas are introduced and we point out some analogies with other branches of mathematics. 1.1 Controlled differential equations Differential equations are omnipresent in modern pure and applied mathematics; many “pure” disciplines in fact originate in attempts to analyse differential equations from various application areas. Classical ordinary differential equations (ODEs…

## 375 Citations

Controlled Rough Paths on Manifolds I

- Mathematics, Computer Science
- 2015

A theory of push-forwards is presented and it is shown that the integration of a smooth one-form along a manifold valued controlled rough path is in fact well defined independent of any additional geometric structures.

Topics in Stochastic Analysis and Riemannian Foliations

- Mathematics
- 2018

This dissertation contains three research directions. In the first direction, we use rough paths theory to study stochastic differential equations and stochastic partial differential equations. We…

Discretisations of rough stochastic partial differential equations

- Mathematics
- 2016

This thesis consists of two parts, in both of which we consider approximations of rough stochastic PDEs and investigate convergence properties of the approximate solutions. In the first part we use…

Canonical RDEs and general semimartingales as rough paths

- MathematicsThe Annals of Probability
- 2019

In the spirit of Marcus canonical stochastic differential equations, we study a similar notion of rough differential equations (RDEs), notably dropping the assumption of continuity prevalent in the…

Rough path theory via fractional calculus

- Mathematics
- 2018

In this paper, we develop an alternative approach to the fundamental theory of rough paths on the basis of fractional calculus. First, using fractional derivatives, we introduce integration along…

Rough path theory via fractional calculus

- Mathematics
- 2020

In this paper, we develop an alternative approach to the fundamental theory of rough paths on the basis of fractional calculus. First, using fractional derivatives, we introduce integration along…

Rough path theory via fractional calculus

- Mathematics
- 2020

In this paper, we develop an alternative approach to the fundamental theory of rough paths on the basis of fractional calculus. First, using fractional derivatives, we introduce integration along…

Rough path theory via fractional calculus

- Mathematics
- 2020

Infinite Dimensional Rough Dynamics

- Mathematics
- 2016

We review recent results about the analysis of controlled or stochastic differential systems via local expansions in the time variable. This point of view has its origin in Lyons’ theory of rough…

Causal Functional Calculus

- Mathematics
- 2019

We construct a new topology on the space of right continuous paths with left limits (càdlàg paths) and introduce a calculus for causal functionals on generic domains of this space. We propose a…

## References

Introduction to KPZ

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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…