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.
|Number of pages||24|
|Journal||Osaka Journal of Mathematics|
|Publication status||Published - 2016 Jul|
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