- Date: 20 Apr. (Thu.)
- Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
- Time: 16:30 – 18:00
- Speaker: Thomas Cavalazzi (Université de Rennes 1)
- Title: Quantitative weak propagation of chaos for McKean-Vlasov SDEs driven by $\alpha$-stable processes
- Abstract:
In this talk, we will deal with McKean-Vlasov Stochastic Differential Equations (SDEs) driven by $\alpha$-stable processes, with $\alpha \in (1,2)$. We make Hölder-type assumptions on the coefficients, with respect to both space and measure variables.
We will study the associated semi-group, acting on functions defined on the space of probability measures, through the related backward Kolmogorov Partial Differential Equation (PDE), which describes its dynamics.
We will focus in particular on its regularizing properties.
The study relies on differential calculus for functions defined on the space of measures, and on Itô’s formula along flows of marginal distributions of jump processes defined with Poisson random integrals.
We will finally use the preceding tools to prove quantitative weak propagation of chaos for the mean-field interacting particle system associated with the McKean-Vlasov SDE.
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