Heat kernel of supercritical SDEs with unbounded drifts

Stéphane Menozzi, Zhang Xicheng

Let $\alpha \in (0,2)$ and $d\in \mathbb{N}$. Consider the following SDE in ${\mathbb{R}}^d$:$$\mathrm{d}{X}_t=b(t,X_t)\mathrm{d}t+a(t,X_{t-})\mathrm{d}{L}_t^{(\alpha )},X_0=x,$$where $L^{(\alpha )}$ is a $d…