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dc.contributor.authorGeiss, Stefan
dc.contributor.authorYlinen, Juha
dc.date.accessioned2021-02-18T07:34:36Z
dc.date.available2021-02-18T07:34:36Z
dc.date.issued2021
dc.identifier.citationGeiss, S., & Ylinen, J. (2021). Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs. <i>Memoirs of the American Mathematical Society</i>, <i>272</i>(1335), 1-112. <a href="https://doi.org/10.1090/memo/1335" target="_blank">https://doi.org/10.1090/memo/1335</a>
dc.identifier.otherCONVID_28870790
dc.identifier.otherTUTKAID_80375
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/74282
dc.description.abstractWe introduce a decoupling method on the Wiener space to define a wide class of anisotropic Besov spaces. The decoupling method is based on a general distributional approach and not restricted to the Wiener space. The class of Besov spaces we introduce contains the traditional isotropic Besov spaces obtained by the real interpolation method, but also new spaces that are designed to investigate backwards stochastic differential equations (BSDEs). As examples we discuss the Besov regularity (in the sense of our spaces) of forward diffusions and local times. It is shown that among our newly introduced Besov spaces there are spaces that characterize quantitative properties of directional derivatives in the Malliavin sense without computing or accessing these Malliavin derivatives explicitly. Regarding BSDEs, we deduce regularity properties of the solution processes from the Besov regularity of the initial data, in particular upper bounds for their Lpvariation, where the generator might be of quadratic type and where no structural assumptions, for example in terms of a forward diffusion, are assumed. As an example we treat sub-quadratic BSDEs with unbounded terminal conditions. Among other tools, we use methods from harmonic analysis. As a by-product, we improve the asymptotic behaviour of the multiplicative constant in a generalized Fefferman inequality and verify the optimality of the bound we established.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherAmerican Mathematical Society
dc.relation.ispartofseriesMemoirs of the American Mathematical Society
dc.rightsCC BY-NC-ND 4.0
dc.subject.otherAnisotropic Besov spaces
dc.subject.otherdecoupling on the Wiener space
dc.subject.otherbackward stochastic differential equations
dc.subject.otherinterpolation
dc.titleDecoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202102171689
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2021-02-17T16:15:03Z
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange1-112
dc.relation.issn0065-9266
dc.relation.numberinseries1335
dc.relation.volume272
dc.type.versionacceptedVersion
dc.rights.copyright© American Mathematical Society, 2019
dc.rights.accesslevelopenAccessfi
dc.subject.ysostokastiset prosessit
dc.subject.ysoosittaisdifferentiaaliyhtälöt
dc.subject.ysofunktionaalianalyysi
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p11400
jyx.subject.urihttp://www.yso.fi/onto/yso/p12392
jyx.subject.urihttp://www.yso.fi/onto/yso/p17780
dc.rights.urlhttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi10.1090/memo/1335
dc.type.okmA1


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