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Unimodal Levy Processes on Bounded Lipschitz Sets

We give asymptotics near the boundary for the distribution of the first exit time of the isotropic alpha-stable Levy process on bounded Lipschitz sets in real euclidean space. These asymptotics bear some relation to the existence of limits in the Yaglom sense of alpha-stable processes. Our approach relies on the uniform integrability of the ratio of Green functions on bounded Lipschitz sets.

We use bounds for the heat remainder to give the first two terms in the small time asymptotic expansion of the trace of the heat kernel of unimodal Levy processes satisfying some weak scaling conditions on bounded Lipschitz domains.

Identiferoai:union.ndltd.org:uoregon.edu/oai:scholarsbank.uoregon.edu:1794/23725
Date06 September 2018
CreatorsArmstrong, Gavin
ContributorsSinclair, Christopher
PublisherUniversity of Oregon
Source SetsUniversity of Oregon
Languageen_US
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
RightsAll Rights Reserved.

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