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 $\hat{I}\pm$-stable processes with respect to the index $\hat{I}\pm \in [\hat{I}{\pm }_0,2]$ for some $\hat{I}{\pm }_0>0$. In addition, we estima…