390022 VO Rough Paths (2022W)
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Details
Language: English
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
Thursday
06.10.
15:00 - 16:30
Seminarraum 5, Kolingasse 14-16, EG00
Thursday
13.10.
15:00 - 16:30
Seminarraum 5, Kolingasse 14-16, EG00
Thursday
20.10.
15:00 - 16:30
Seminarraum 5, Kolingasse 14-16, EG00
Thursday
27.10.
15:00 - 16:30
Seminarraum 5, Kolingasse 14-16, EG00
Thursday
03.11.
15:00 - 16:30
Seminarraum 5, Kolingasse 14-16, EG00
Thursday
10.11.
15:00 - 16:30
Seminarraum 5, Kolingasse 14-16, EG00
Thursday
17.11.
15:00 - 16:30
Seminarraum 5, Kolingasse 14-16, EG00
Thursday
24.11.
15:00 - 16:30
Seminarraum 5, Kolingasse 14-16, EG00
Thursday
01.12.
15:00 - 16:30
Seminarraum 5, Kolingasse 14-16, EG00
Thursday
15.12.
15:00 - 16:30
Seminarraum 5, Kolingasse 14-16, EG00
Thursday
12.01.
15:00 - 16:30
Seminarraum 5, Kolingasse 14-16, EG00
Thursday
19.01.
15:00 - 16:30
Seminarraum 5, Kolingasse 14-16, EG00
Thursday
26.01.
15:00 - 16:30
Seminarraum 5, Kolingasse 14-16, EG00
Information
Aims, contents and method of the course
Assessment and permitted materials
Oral exam
Minimum requirements and assessment criteria
Prerequisites:
The aim will be to make the course as self-contained as possible, but some knowledge of stochastic analysis and a basic understanding of stochastic integration is recommended. Knowledge about the construction of the Ito integral would be ideal, but is not strictly required.Lecture Notes:
https://ucloud.univie.ac.at/index.php/s/xSJDcFaz5i2AGAE
The aim will be to make the course as self-contained as possible, but some knowledge of stochastic analysis and a basic understanding of stochastic integration is recommended. Knowledge about the construction of the Ito integral would be ideal, but is not strictly required.Lecture Notes:
https://ucloud.univie.ac.at/index.php/s/xSJDcFaz5i2AGAE
Examination topics
Content of the lectures
Reading list
Literature:
Friz, Peter K., and Martin Hairer. A course on rough paths. Springer International Publishing, 2020.
Friz, Peter K., and Nicolas B. Victoir. Multidimensional stochastic processes as rough paths: theory and applications. Vol. 120. Cambridge University Press, 2010.
T. Lyons: St. Flour Lectures on Rough Path Theory
Hairer, Martin, and David Kelly. "Geometric versus non-geometric rough paths." Annales de l'IHP Probabilités et statistiques. Vol. 51. No. 1. 2015.
Friz, Peter K., and Martin Hairer. A course on rough paths. Springer International Publishing, 2020.
Friz, Peter K., and Nicolas B. Victoir. Multidimensional stochastic processes as rough paths: theory and applications. Vol. 120. Cambridge University Press, 2010.
T. Lyons: St. Flour Lectures on Rough Path Theory
Hairer, Martin, and David Kelly. "Geometric versus non-geometric rough paths." Annales de l'IHP Probabilités et statistiques. Vol. 51. No. 1. 2015.
Association in the course directory
Last modified: Th 23.11.2023 09:08
The aim of this course is to provide an introduction to the theory of rough paths, with a particular focus on their integration theory and associated rough differential equations and how the theory relates to and enhances the field of stochastic calculus.Our first motivation will be to understand the limitations of classical notions of integration to handle paths of very low regularity, and to see how the rough integral succeeds where other notions fail.
We will construct rough integrals and establish solutions of differential equations driven by rough paths, as well as the continuity of these objects with respect to the paths involved, and their consistency with stochastic integration and SDEs. We will also consider the class of so called "branched rough paths" and study their rich analytic as well as algebraic foundations, which are essential for understanding more complex theories, such as Martin Haierer's regularity structures.
Various applications and extensions of the theory will then be discussed, such as pathwise stability of likelihood estimators and applications of the stochastic sewing lemma.Aim:
Participants will be familiar with rough/Young integration of Hölder continuous processes/functions and able to solve simple differential equations with rough drivers, as well as being aware of the pro's and con's of the theory.
In addition to the probabilistic and analytic aspects, participants will have also gained an elementary knowledge of the algebraic setting related to Hopf-algebras.