A class of singular symmetric Markov processes
A class of Lévy-type jump processes on \(\mathbb R^d\) with jump kernel of type \[ J(x,y):= 1_{\{x_i\neq y_i, i\leq d\}}\frac{c(x,y)}{|x-y|^{1+\alpha}} \] is investigated, where \(\alpha \in (0,2)\) is a constant, and \(k_1\leq c(x,y)\leq k_2\) holds for some constants \(k_1,k_2>0.\) Explicit upper and lower bounds are derived for the heat kernel and the bounded harmonic functions are proved to be Hölder continuous.
scientific article; zbMATH DE number 6136703
scientific article