Seminar: Rough Paths

 Seminar Winter Term 2016/2017


Rough Paths

 

Lecturer:
Robert Stelzer, Karsten Urban, Thai Nguyen
Type:Master (all mathematical programmes including Finance)
Registration:
To register for the seminar, please write an E-Mail to Eva Nacca  until  July 13th, 2016, 11:30 a.m. In the e-mail please give your name,  matriculation number, your course of studies and subjects you have taken in the area of Financial Mathematics, Numerical Mathematics or Probability. The number of participants is limited to 15 students.
Content:

In this seminar we shall together work on understanding the modern rough path integration theory (for stochastic integrals) and its application in rough (partial) differential equations based on a textbook coauthored by a fields medaillist.

The books back cover text:

"Lyons’ rough path analysis has provided new insights in the analysis of stochastic differential equations and stochastic partial differential equations, such as the KPZ equation. This textbook presents the first thorough and easily accessible introduction to rough path analysis.

When applied to stochastic systems, rough path analysis provides a means to construct a pathwise solution theory which, in many respects, behaves much like the theory of deterministic differential equations and provides a clean break between analytical and probabilistic arguments. It provides a toolbox allowing to recover many classical results without using specific probabilistic properties such as predictability or the martingale property. The study of stochastic PDEs has recently led to a significant extension – the theory of regularity structures – and the last parts of this book are devoted to a gentle introduction.

Most of this course is written as an essentially self-contained textbook, with an emphasis on ideas and short arguments, rather than pushing for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis courses and has some interest in stochastic analysis. For a large part of the text, little more than Itô integration against Brownian motion is required as background." (quoted from http://www.springer.com/de/book/9783319083315 )

 

   
First meeting
(assignment of topics):
July 13th, 2016, 15:05 (sharp!), Heho 22, E18
Prerequisites:

An Introduction to Probability and Statistics, Stochastik 2

Master in Finance: An Introduction to Measure Theoretic Probability, Stochastics 2

Time and Venue: to be determined
Literature: Friz, Peter K. and Hairer, Martin, A Course On Rough Paths: With An Introduction to Regularity Structures, Springer, Cham, 2014