HEAT KERNEL ESTIMATES FOR SYMMETRIC JUMP PROCESSES WITH MIXED POLYNOMIAL GROWTHS

• 成果类型: Article
• 署名作者: Bae, Joohak; Kang, Jaehoon; Kim, Panki; Lee, Jaehun
• 署名单位: Seoul National University (SNU); University of Bielefeld; Seoul National University (SNU)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1323
• 发表日期: 2019
• 页码: 2830-2868
• 关键词: dirichlet forms; upper-bounds; density; PROPERTY; LAWS

摘要

In this paper, we study the transition densities of pure-jump symmetric Markov processes in 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 the transition densities (heat kernel estimates) for such processes. This is the first study on global heat kernel estimates of jump processes (including non-Levy 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 infinity.