Wednesday, July 22, 2026 - 14:00 in V3-201+Zoom
Exponential Ergodicity for McKean-Vlasov SDEs with Singular Interactions
A talk in the Bielefeld Stochastic Afternoon series by
Xing Huang from Tianjin University
| Abstract: |
Let $k\in (d,\infty]$ and consider the $k*$-distance
$$\|\mu-\nu\|_{k*}:= \sup\Big\{|\mu(f)-\nu(f)|:\ f\in\B_b(\mathbb{R}^d),\
\|f\|_{\tt L^k}:=\sup_{x\in \mathbb{R}^d}\|1_{B(x,1)}f\|_{L^k}\le 1\Big\}$$
between probability measures on $\mathbb{R}^d$. The exponential ergodicity in
$1$-Wasserstein and $k*$-distances is derived
for a class of McKean-Vlasov SDEs with small singular interactions
measured by $\|\cdot\|_{k*}.$ Moreover, the exponential ergodicity in
$2$-Wasserstein distance and relative entropy is derived when the
interaction term is given by
$$b^{(0)}(x,\mu) :=\int_{\mathbb{R}^d}h(x-y)\mu(d y)$$ for some measurable
function $h: \mathbb{R}^d \to \mathbb{R}^d$ with small $\|h\|_{\tt L^k}$.
Within the CRC this talk is associated to the project(s): A5, B1 |
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