Heat kernel estimates for symmetric jump processes with mixed polynomial growths

Abstract

In this paper, we study the transition densities of pure-jump symmetric Markov processes in ${\mathbb{R}}^d$, whose jumping kernels are comparable to radially symmetric functions with mixed polynomial growths. Under some mild assumptions on their scale functions, we establish sharp two-sided estimates of transition densities (heat kernel estimates) for such processes. This is the first study on global heat kernel estimates of jump processes (including non-Lévy processes) whose weak scaling index is not necessarily strictly less than 2. As an application, we proved that the finite second moment condition on such symmetric Markov process is equivalent to the Khintchine-type law of iterated logarithm at the infinity.

arXiv comment50 pages

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Cited by in corpus (2)

• Heat kernel estimates for general symmetric pure jump Dirichlet forms
• Heat kernel estimates and their stabilities for symmetric jump processes with general mixed polynomial growths on metric measure spaces