Transition probability estimates for subordinate random walks

Abstract

Let $S_n$ be the simple random walk on the integer lattice ${\mathbb{Z}}^d$. For a Bernstein function $\varphi$ we consider a random walk $S_n^{\varphi }$ which is subordinated to $S_n$. Under a certain assumption on the behaviour of $\varphi$ at zero we establish global estimates for the transition probabilities of the random walk $S_n^{\varphi }$. The main tools that we apply are the parabolic Harnack inequality and appropriate bounds for the transition kernel of the corresponding continuous time random walk.

arXiv commentTo appear in Mathematische Nachrichten