Instructor: Jan Maas
Teaching Assistant: Giovanni Zanco
Stochastic partial differential equations (SPDEs) are used to model a wide variety of physical systems subject to randomness or noise. In many interesting situations, solutions to SPDEs are very irregular, which makes their analysis particularly challenging. In the last couple of years, spectacular progress has been obtained through the use of "rough paths theory" and the development of the theory of "regularity structures", for which M. Hairer has been awarded a Fields Medal. In this course we aim to give a gentle introduction to SPDEs with a special emphasis on these recent developments.
Background knowledge in analysis and/or probability theory will be helpful but is not required.
* P. Friz and M. Hairer, A course on rough paths
* M. Hairer, An introduction to stochastic PDEs
* M. Hairer, Introduction to Regularity Structures
* M. Hairer, Regularity structures and the dynamical Φ_4^3 model
The final grade is based on homework (50%) and the oral exam (50%).
|Oct 8||Young integration|
|Oct 13||Solving Young ODEs; definition of a rough path|
|Oct 15||Controlled rough paths|
|Oct 20||Sewing lemma; integration of controlled rough paths|
|Oct 22||Fundamental theorem of calculus, Itô-Stratonovich correction, and Itô formula for rough integration|
|Nov 3||Brownian motion; Kolmogorov continuity criterion|
|Nov 5||Brownian motion as a rough path; stochastic differential equations|
|Nov 10||Stochastic heat equation|
To take a look at the additional Downloads, please click here. (you must be logged in!)