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Mini-course "McKean-Vlasov SDEs, Particle Systems and Calculus on Wasserstein Space" Lukasz Szpruch

Event ended

Laboratory of Stochastic Analysis and its Applications invites you to mini-course:"McKean-Vlasov SDEs, Particle Systems and Calculus on Wasserstein Space"   Lukasz Szpruch, assistant professor of School of Mathematics, University of Edinburgh, The Alan Turing Institute (London)

Mini-course will be held on April 02, 04 and 06

Location: Moscow, 26 Shabolovka st., room: 3102

 

Schedule of mini-course:
02 April - 18:00 - 21:00 room 3102
05 April - 18:00 - 21:00 room 3102
06 April - 18:00 - 21:00 room 3102

Abstract 

In his lectures at the College de France Lions demonstrated that the key tool to study Mean-Field Games is a new class of PDEs that describe the evolution of functions of measures. The new concept of a derivative with respect to the measure opened a new research field that impacts a large landscape of mathematics beyond Mean-Field Games: from Stochastic Analysis to Optimal Transport. It turns out that similar concepts to calculus on Wasserstein space allowed for a breakthrough in Kac’s programme in Kinetic Theory. In this course I will present the concept of Lions derivative and will show its consequences on study of McKean-Vlasov SDEs.

Program

1 From Particle Systems to McKean-Vlasov SDEs

1.1 Examples and area of applications

1.2 Well-posedness results via Fixed point

1.3 Well-posedness results via propagation of chaos - martingale problem

1.4 General compactness argument

1.5 Associated PDEs

2 Calculus of Wasserstein Space

2.1 Lions Derivative

2.2 Basic examples

2.3 Itô formula for functions of measures

2.4 PDEs on measure space

2.5 Regularisation by noise and a fixed point

2.6 A new perspective on Martingale problem

3 Applications

3.1 Mean-Filed Games

3.2 Mimicking Theorem by Gyöngy

The course is open to anyone interested. Whether you need the pass to the Higher School of Economics, do not hesitate to contact the lab manager Julia Pavlyuk ypavlyuk@hse.ru