Global heat kernel estimates for symmetric jump processes

Abstract

In this paper, we study sharp heat kernel estimates for a large class of symmetric jump-type processes in ℝd for all t > 0. A prototype of the processes under consideration are symmetric jump processes on ℝd with jumping intensity where ν is a probability measure on [α1, α2] ⊂ (0, 2), Φ is an increasing function on [0,∞) with β Ie{cyrillic, ukrainian} (0,∞), and c(α, x, y) is a jointly measurable function that is bounded between two positive constants and is symmetric in (x, y). They include, in particular, mixed relativistic symmetric stable processes on ℝd with different masses. We also establish the parabolic Harnack principle. © 2011 Zhen-Qing Chen, Panki Kim, and Takashi Kumagai.