TY - JOUR
T1 - On instability of global path properties of symmetric dirichlet forms under Mosco-convergence
AU - Suzuki, Kohei
AU - Uemura, Toshihiro
N1 - Funding Information:
The first author was supported by Grant-in-Aid for JSPS Fellows Number 261798 and the SGU program in Kyoto university. The second author was supported by Grant-in-Aid for Scientific Research (C) Number 15K04941.
Publisher Copyright:
© 2016, Osaka Journal of Mathematics. All Rights Reserved.
PY - 2016/7
Y1 - 2016/7
N2 - 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.
AB - 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.
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M3 - Article
AN - SCOPUS:84982980473
SN - 0030-6126
VL - 53
SP - 567
EP - 590
JO - Osaka Journal of Mathematics
JF - Osaka Journal of Mathematics
IS - 3
ER -