Wednesday, May 10, 2023 - 16:15 in V3-201 + Zoom
Heat kernel estimates for stable-driven SDEs with Besov distributional drift
A talk in the Bielefeld Stochastic Afternoon series by
Mathis Fitoussi
| Abstract: |
we are interested in computing heat kernel estimates for
stochastic differential equations with singular time-inhomogeneous drift
in $L^r - B^β_{p,q}$ driven by a symmetric d-dimensional $\alpha$-stable
process, $\alpha \in (1, 2)$. We show that, when $\beta > (1− \alpha + \alpha /r +
d/p)/2$, the martingale solution associated with this SDE admits a
density which enjoys two-sided heat kernel bounds as well as gradient
estimates w.r.t. the backward variable. Our approach relies on a
mollification of the drift and the use of Besov space properties (mainly
thermic characterization, duality and product rules).
Within the CRC this talk is associated to the project(s): B1 |
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