• FU-Students should register via Campus Management.
• Non-FU-students should register via MyCampus/Whiteboard.

Summer Term 2025

lecture and exercise by Dr. Guilherme de Lima Feltes

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Time and place

• Lecture: Wednesdays, 10:00 -12:00, SR 009, Arnimallee 6.

• Exercise Session: Wednesdays, 12:00 -14:00, SR 009, Arnimallee 6.

• Final Exam:  to be announced in due course

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Prerequisits: Stochastics I, II, III. Recommended: Functional Analysis..

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)   

Exercises 

Problem sets will be put online under Assignements in the Whiteboard portal. The solutions will be discussed in the tutorial.

Course Overview/ Content:

We will learn two different methods for solving stochastic partial differential equations. The classical method is based on Ito calculus, and we will use it to solve semilinear SPDEs with space-time white noise in one space dimension. But we will see that in higher dimensions this theory only works for linear equations, and motivated by that we will introduce "paracontrolled distributions“, which we developed in the last years based on ideas from harmonic analysis and rough paths, and which allow us to solve some interesting semilinear equations in higher dimensions. Along the way we will learn about regularity theory for semilinear PDEs, Gaussian Hilbert spaces, and much more.

• Ito calculus for Gaussian random measures;
• semilinear stochastic PDEs in one dimension;
• Schauder estimates;
• Gaussian hypercontractivity;
• paraproducts and paracontrolled distributions;
• local existence and uniqueness for semilinear SPDEs in higher dimensions;
• properties of solutions

References

• There will be lecture notes