On Pathwise Stochastic Integration of Processes with Unbounded Power Variation

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.advisorViitasaari, Lauri, Dr., Aalto University, Department of Mathematics and Systems Analysis, Finland
dc.contributor.authorChen, Zhe
dc.contributor.departmentMatematiikan ja systeemianalyysin laitosfi
dc.contributor.departmentDepartment of Mathematics and Systems Analysisen
dc.contributor.labStochastics and Statisticsen
dc.contributor.schoolPerustieteiden korkeakoulufi
dc.contributor.schoolSchool of Scienceen
dc.contributor.supervisorLeskelä, Lasse, Prof., Aalto University, Department of Mathematics and Systems Analysis, Finland
dc.date.accessioned2016-02-19T10:01:22Z
dc.date.available2016-02-19T10:01:22Z
dc.date.defence2016-03-11
dc.date.issued2016
dc.description.abstractThis dissertation concerns pathwise integrability of stochastic processes which are non-semimartingales with unbounded power variation. In this dissertation, a class of stochastic processes which can be represented as a composition of a Hölder continuous process with a nonrandom function of locally bounded variation is studied. Since the nonrandom function may contain discontinuities, stochastic processes in this class are usually of unbounded power variation. This kind of stochastic processes are of interest in many applications, for example in financial mathematics concerning option pricing. In this dissertation, new conditions are presented for the existence of generalized Lebesgue–Stieltjes integrals for the aforementioned one-dimensional stochastic processes with respect to general Hölder continuous processes. This dissertation also contains a new result on the existence of generalized Lebesgue–Stieltjes integrals for a certain class of multi-dimensional stochastic processes with respect to general Hölder continuous processes. Moreover, in this dissertation, a new proof is presented for a change of variables formula for sufficiently regular one-dimensional stochastic processes with unbounded power variation.en
dc.format.extent103
dc.format.mimetypeapplication/pdfen
dc.identifier.isbn978-952-60-6672-1 (electronic)
dc.identifier.isbn978-952-60-6671-4 (printed)
dc.identifier.issn1799-4942 (electronic)
dc.identifier.issn1799-4934 (printed)
dc.identifier.issn1799-4934 (ISSN-L)
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/19773
dc.identifier.urnURN:ISBN:978-952-60-6672-1
dc.language.isoenen
dc.opnSottinen, Tommi, Prof., University of Vaasa, Finland
dc.publisherAalto Universityen
dc.publisherAalto-yliopistofi
dc.relation.ispartofseriesAalto University publication series DOCTORAL DISSERTATIONSen
dc.relation.ispartofseries34/2016
dc.revSalminen, Paavo, Prof., Åbo Akademi University, Finland
dc.revShevchenko, Georgiy, Prof., Taras Shevchenko National University of Kyiv, Ukraine
dc.subject.keywordpathwise integrationen
dc.subject.keywordHölder processen
dc.subject.keywordunbounded p-variationen
dc.subject.keywordgeneralized Lebesgue-Stieltjes integrationen
dc.subject.otherMathematicsen
dc.titleOn Pathwise Stochastic Integration of Processes with Unbounded Power Variationen
dc.typeG4 Monografiaväitöskirjafi
dc.type.dcmitypetexten
dc.type.ontasotDoctoral dissertation (monograph)en
dc.type.ontasotVäitöskirja (monografia)fi
local.aalto.archiveyes
local.aalto.digiauthask
local.aalto.digifolderAalto_64851
local.aalto.formfolder2016_02_19_klo_11_08
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