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

Kohei Suzuki, Toshihiro Uemura

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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 L1(ℝd; dx)-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.

Original languageEnglish
Pages (from-to)567-590
Number of pages24
JournalOsaka Journal of Mathematics
Volume53
Issue number3
Publication statusPublished - 2016 Jul

ASJC Scopus subject areas

  • Mathematics(all)

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