{"title":"Tanaka formula for strictly stable processes","authors":"H. Tsukada","doi":"10.19195/0208-4147.39.1.3","DOIUrl":null,"url":null,"abstract":"For symmetric Levy processes, if the local times exist, the Tanaka formula has already been constructed via the techniques in the potential theory by Salminen and Yor 2007. In this paper, we study the Tanaka formula for arbitrary strictly stable processes with index α ∈ 1, 2, including spectrally positive and negative cases in a framework of Ito’s stochastic calculus. Our approach to the existence of local times for such processes is different from that of Bertoin 1996.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.19195/0208-4147.39.1.3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
For symmetric Levy processes, if the local times exist, the Tanaka formula has already been constructed via the techniques in the potential theory by Salminen and Yor 2007. In this paper, we study the Tanaka formula for arbitrary strictly stable processes with index α ∈ 1, 2, including spectrally positive and negative cases in a framework of Ito’s stochastic calculus. Our approach to the existence of local times for such processes is different from that of Bertoin 1996.
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