Show simple item record

dc.contributorCabré Vilagut, Xavier
dc.contributorCortés López, Juan Carlos
dc.contributor.authorJornet Sanz, Marc
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
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.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.rights.accessRestricted access - author's decision
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística

Files in this item


This item appears in the following Collection(s)

Show simple item record

All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder