401-4611-66L Rough Path Theory and Regularity Structures
|Semester||Autumn Semester 2016|
|Lecturers||J. Teichmann, D. Prömel|
|Language of instruction||English|
|Abstract||The course provides an introduction to the theory of controlled rough paths with focus on stochastic differential equations. In parallel, Martin Hairer's new theory of regularity structures is introduced taking controlled rough paths as guiding examples. In particular, the course demonstrates how to use the theory of regularity structures to solve singular stochastic PDEs.|
|Objective||The main goal is to develop simultaneously the basic concepts of rough path theory and Hairer's regularity structures.|
|Literature||- Peter Friz and Martin Hairer, A Course on Rough Paths: With an Introduction to|
Regularity Structures, Springer, 2014.
- Martin Hairer, Introduction to regularity structures, Braz. J. Probab. Stat. 29 (2015),
no. 2, 175-210.
- Peter Friz and Nicolas Victoir, Multidimensional stochastic processes as rough paths.
Theory and applications, Cambridge University Press, 2010.
- Martin Hairer, A theory of regularity structures, Inventiones mathematicae (2014), 1-236.
- Ajay Chandra and Hendrik Weber, Stochastic PDEs, Regularity Structures, and Inter-
acting Particle Systems, Preprint arXiv:1508.03616.
|Prerequisites / Notice||Requirements: Brownian Motion and Stochastic Calculus|