On instability of global path properties of symmetric Dirichlet forms under Mosco-convergence

Suzuki, Kohei; Uemura, Toshihiro

Abstract

We give sufficient conditions for Mosco convergences for the following three cases: symmetric locally uniformly elliptic diffusions, symmetric Lévy processes, and symmetric jump processes in terms of the L 1 (Ê d Á d x)-local convergence of the (elliptic) coefficients, the characteristic exponents and the jump density functions, respectively. We stress that the global path properties of the corresponding Markov processes such as recurrence/transience, and conservativeness/explosion are not preserved under Mosco convergences and we give several examples where such situations indeed happen.

Citation

Suzuki, K., & Uemura, T. (2016). On instability of global path properties of symmetric Dirichlet forms under Mosco-convergence. Osaka Journal of Mathematics, 53(3), 567-590. https://doi.org/10.18910/58908

• Journal Article Type: Article
• Acceptance Date: Oct 16, 2014
• Publication Date: Aug 5, 2016
• Deposit Date: Oct 20, 2024
• Journal: Osaka Journal of Mathematics
• Print ISSN: 0030-6126
• Publisher: Departments of Mathematics of Osaka University and Osaka City University
• Peer Reviewed: Peer Reviewed
• Volume: 53
• Issue: 3
• Pages: 567-590
• DOI: https://doi.org/10.18910/58908
• Public URL: https://durham-repository.worktribe.com/output/2977820