@article{68d69c63f075427ab67b6f10f0b9c83e,
title = "On the conservativeness and the recurrence of symmetric jump-diffusions",
abstract = "Sufficient conditions for a symmetric jump-diffusion process to be conservative and recurrent are given in terms of the volume of the state space and the jump kernel of the process. A number of examples are presented to illustrate the optimality of these conditions; in particular, the situation is allowed to be that the state space is topologically disconnected but the particles can jump from a connected component to the other components.",
keywords = "Conservation property, Integral-derivation property, Jump process, Recurrence, Regular Dirichlet form",
author = "Jun Masamune and Toshihiro Uemura and Jian Wang",
note = "Funding Information: Part of this work was done when J. Masamune and J. Wang visited TU Dresden as a visitor and a Humboldt fellow, respectively. They are grateful to Professor Ren{\'e} L. Schilling for providing them with nice working environment and for stimulating discussions. J. Masamune also would like to express his sincere gratitude to Professor Umberto Mosco for several inspiring discussions and acknowledge the support by the National Science Foundation Grant No. 1109356. J. Wang also gratefully acknowledges the financial support through National Natural Science Foundation of China (No. 11126350 and 11201073) and the Program for Excellent Young Talents and for New Century Excellent Talents in Universities of Fujian (No. JA10058, JA11051 and JA12053).",
year = "2012",
month = dec,
day = "15",
doi = "10.1016/j.jfa.2012.09.014",
language = "English",
volume = "263",
pages = "3984--4008",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "12",
}