Malliavin Calculus for Chaos Expansions of Generalized Stochastic Processes with Applications to Some Classes of Differential Equations

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Malliavin Calculus for Chaos Expansions of Generalized Stochastic Processes with Applications to Some Classes of Differential Equations

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dc.contributor.advisor Seleši, Dora
dc.contributor.author Levajković, Tijana
dc.date.accessioned 2014-06-27T10:39:21Z
dc.date.available 2014-06-27T10:39:21Z
dc.date.issued 2011
dc.identifier.uri http://hdl.handle.net/123456789/3824
dc.description.abstract In this dissertation we study the main properties of the operators of Malliavin calculus de ned on a set of singular generalized stochastic processes, which admit chaos expansion representation form in terms of orthogonal polynomial basis and having values in a certain weighted space of stochastic distributions in white noise framework. In the rst part of the dissertation we focus on white noise spaces and introduce the fractional Poissonian white noise space. All four types of white noise spaces obtained (Gaussian, Poissonian, fractional Gaussian and fractional Poissonian) can be identi ed through unitary mappings. As a contribution to the Malliavin di erential theory, theorems which characterize the operators of Malliavin calculus, extended from the space of square integrable random variables to the space of generalized stochastic processes were obtained. Moreover the connections with the corresponding fractional versions of these operators are emphasized and proved. Several examples of stochastic di erential equations involving the operators of the Malliavin calculus, solved by use of the chaos expansion method, have found place in the last part of the dissertation. Particularly, obtained results are applied to solving a generalized eigenvalue problem with the Malliavin derivative and a stochastic Dirichlet problem with a perturbation term driven by the Ornstein-Uhlenbeck operator. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2014-06-27T10:39:21Z No. of bitstreams: 1 DR_Tijana.pdf: 1518875 bytes, checksum: 696b3c7c2245c1881f85b8c5f28f724f (MD5) en
dc.description.provenance Made available in DSpace on 2014-06-27T10:39:21Z (GMT). No. of bitstreams: 1 DR_Tijana.pdf: 1518875 bytes, checksum: 696b3c7c2245c1881f85b8c5f28f724f (MD5) Previous issue date: 2011 en
dc.language.iso en en_US
dc.publisher Novi Sad en_US
dc.title Malliavin Calculus for Chaos Expansions of Generalized Stochastic Processes with Applications to Some Classes of Differential Equations en_US
mf.author.birth-date 1974-01-01
mf.author.birth-place Beograd en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srpska en_US
mf.subject.area Mathematics en_US
mf.subject.keywords Generalized stochastic processes, white noise, Brownian motion, fractional white noise, fractional Brownian motion, Poisson process, Poissonian white noise, fractional Poissonian process, L evy process, chaos expansion, Fourier-Hermite polynomials, Charlier polyno mials,integral, Ornstein-Uhlenbeck operator, stochastic di erential equations, Sobolev spaces, Kondratiev spaces, weighted spaces of stochastic distributions,Hilbert spaces, linear elliptic di erential operator, Fredholm alternative, Dirichlet problem. en_US
mf.subject.subarea Analysis and probability en_US
mf.university.faculty FACULTY OF SCIENCE en_US
mf.document.references 70 en_US
mf.document.pages 197 en_US
mf.document.location Novi Sad en_US
mf.document.genealogy-project No en_US
mf.university UNIVERSITY OF NOVI SAD en_US

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