The Non-Gaussian to Gaussian Transition: Pointwise Heat Kernel Estimates and Optimal Convergence Rates

Xianming Liu, Chongyang Ren, Mingyan Wu

We establish uniform pointwise estimates for the densities of a family of $\alpha$-stable processes with respect to the index $\alpha \in [{\alpha }_0,2]$ for some ${\alpha }_0>0$. In addition, we estimate t…