@article{75135dab49aa425abae3bccaa0ddc264,
title = "Laws of the iterated logarithm for symmetric jump processes",
abstract = "Based on two-sided heat kernel estimates for a class of symmetric jump processes on metric measure spaces, the laws of the iterated logarithm (LILs) for sample paths, local times and ranges are established. In particular, the LILs are obtained for β-stable-like processes on α-sets with β >0.",
keywords = "Law of the iterated logarithm, Local time, Range, Sample path, Stable-like process, Symmetric jump processes",
author = "Panki Kim and Takashi Kumagai and Jian Wang",
note = "Funding Information: Our first proof of Proposition 4.8 was under assumption of some scaling property on the space. We thank D. Croydon, C. Nakamura and Y. Shiozawa for useful comments, and we also thank Professor Zhen-Qing Chen for the proof of Proposition 2.5. The authors are also indebted to two referees for their helpful comments and careful corrections. The research of Panki Kim is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. NRF-2015R1A4A1041675). The research of Takashi Kumagai is partially supported by the Grant-in-Aid for Scientific Research (A) 25247007, Japan. The research of Jian Wang is supported by National Natural Science Foundation of China (No. 11201073 and 11522106), the JSPS postdoctoral fellowship (26-04021), and the Program for Nonlinear Analysis and Its Applications (No. IRTL1206). Publisher Copyright: {\textcopyright} 2017 ISI/BS.",
year = "2017",
month = nov,
doi = "10.3150/16-BEJ812",
language = "English",
volume = "23",
pages = "2330--2379",
journal = "Bernoulli",
issn = "1350-7265",
publisher = "International Statistical Institute",
number = "4A",
}