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

Kohei Suzuki, Toshihiro Uemura

研究成果: Article査読

2 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)567-590
ページ数24
ジャーナルOsaka Journal of Mathematics
53
3
出版ステータスPublished - 2016 7

ASJC Scopus subject areas

  • 数学 (全般)

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