Springe direkt zu Inhalt

19242101 Aufbaumodul: Stochastics IV "Stochastic Partial Differential Equations: Classical and New"

Summer Term 2022

Lecture: Dr. Willem van Zuijlen
Exercise: Dr. Immanuel Zachhuber


Time and place

  • Lecture: Tuesday,  16:00 - 18:00h, SR 025/026, Arnimallee 6.
                   The first meeting is on Tuesday, 19.04. The lecture will take place in Hybrid form, the details for the online-meeting will be available in Whiteboard. If you do not have access to Whiteboard (yet), please send me an email. 

  • Exercise Session: Wednesdays, 10:00 - 12:00h, SR 009, Arnimallee 6.

  • Final Exam:  to be announced in due course

Prerequisits: Stochastics I—II and Analysis I—III. Recommended: Stochastic Analysis and Functional Analysis. Previous knowledge in PDE theory is not required.

Assessment

To receive credits for the course you need to

  • actively participate in the exercise session 
  • work on and successfully solve the weekly exercises 
  • pass the final exam (see above)

If you are an FU student you only need to register for the course via CM (Campus Management).
If you are not an FU student, you are required to register via MyCampus/Whiteboard.    

Exercises 

Problem sets will be put online every Wednesday and can be found under Assignements in the MyCampus/Whiteboard portal. You do not have to submit your solutions. The solutions will be discussed in the online tutorial.

Course Overview/ Content:

  • Ito calculus for Gaussian random measures

  • Semilinear stochastic PDEs in one dimension

  • Basic rough path theory

  • Schauder estimates

  • Gaussian hypercontractivity

  • Paraproducts and paracontrolled distributions

  • Local existence and uniqueness for semilinear SPDEs in higher dimensions

  • Properties of solutions

References

Lecture notes.