Wednesday, July 22, 2026 - 15:15 in V3-201+Zoom
Non-local SDEs, critical drifts and local blow-ups
A talk in the Bielefeld Stochastic Afternoon series by
Chengjun Yue
| Abstract: |
We develop solution theory for SDEs driven by isotropic
alpha-stable process, with general time-inhomogeneous drifts that can
have singularities strong enough to introduce local blow-up effects e.g.
of the type arising in some particle systems with strong attracting
interactions. More specifically, our focus is on weak solutions. We
prove existence and conditional uniqueness (of two kinds) for drifts
satisfying essentially minimal possible critical scaling-invariance
condition. Our approach is based on the fractional Duhamel
representation and new non-local Adams estimates. As a by-product, we
obtain new regularity results for non-local Fokker-Planck equation. This
is joint work with Damir Kinzebulatov.
Within the CRC this talk is associated to the project(s): A5, B1 |
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