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

Summer Term 2020

lecture and exercise by Prof. Dr. Nicolas Perkowski


Time and place

  • Lecture: Video lectures are available online (see below).

  • Exercise Session: Wednesdays, 10:15 - 11:45, online.

  • 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 fo 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 KVV/Whiteboard.    

Exercises 

Problem sets will be put online every Wednesday and can be found under Assignements in the KVV/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 are available in the FU Whiteboard system.

Videos