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dc.contributorCabré Vilagut, Xavier
dc.contributorCortés López, Juan Carlos
dc.contributor.authorJornet Sanz, Marc
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2018-11-02T11:49:58Z
dc.date.issued2018-10
dc.identifier.urihttp://hdl.handle.net/2117/123466
dc.description.abstractRandom differential equations arise to model smooth random phenomena. The error term, instead of being introduced by means of a white noise, arises from imposing randomness to the input coefficients and initial/boundary conditions, with any distribution. We will establish theorems on existence and uniqueness of solution in the $L^p$ setting. We will focus on the first finite-dimensional distributions of the solution stochastic process, with two techniques: the Random Variable Transformation method and Karhunen-Loève expansions. When the probability density function of the response process cannot be computed, it is important to determine the expectation and variance at each time instant. We will give a summary on the main aspects of gPC expansions. The theory introduced in this thesis has permitted writing the following two articles: 10.1016/j.physa.2018.08.024 and 10.22436/jnsa.011.09.06 (article DOIs).
dc.language.isoeng
dc.publisherUniversitat Politècnica de Catalunya
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica
dc.subject.lcshStochastic analysis
dc.subject.otherStochastic system
dc.subject.otherUncertainty quantification
dc.subject.other$\leb^p$ solution
dc.subject.otherProbability density function
dc.subject.otherRandom Variable Transformation technique
dc.subject.otherKarhunen-Loève expansion
dc.subject.otherGeneralized Polynomial Chaos.
dc.titleUncertainty quantification for stochastic systems
dc.typeMaster thesis
dc.subject.lemacAnàlisi estocàstica
dc.subject.amsClassificació AMS::60 Probability theory and stochastic processes::60H Stochastic analysis
dc.identifier.slugFME-1630
dc.rights.accessRestricted access - author's decision
dc.date.lift10000-01-01
dc.date.updated2018-10-24T05:25:32Z
dc.audience.educationlevelMàster
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística


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