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Uncertainty quantification for stochastic systems
dc.contributor | Cabré Vilagut, Xavier |
dc.contributor | Cortés López, Juan Carlos |
dc.contributor.author | Jornet Sanz, Marc |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2018-11-02T11:49:58Z |
dc.date.issued | 2018-10 |
dc.identifier.uri | http://hdl.handle.net/2117/123466 |
dc.description.abstract | Random 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.iso | eng |
dc.publisher | Universitat Politècnica de Catalunya |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica |
dc.subject.lcsh | Stochastic analysis |
dc.subject.other | Stochastic system |
dc.subject.other | Uncertainty quantification |
dc.subject.other | $\leb^p$ solution |
dc.subject.other | Probability density function |
dc.subject.other | Random Variable Transformation technique |
dc.subject.other | Karhunen-Loève expansion |
dc.subject.other | Generalized Polynomial Chaos. |
dc.title | Uncertainty quantification for stochastic systems |
dc.type | Master thesis |
dc.subject.lemac | Anàlisi estocàstica |
dc.subject.ams | Classificació AMS::60 Probability theory and stochastic processes::60H Stochastic analysis |
dc.identifier.slug | FME-1630 |
dc.rights.access | Restricted access - author's decision |
dc.date.lift | 10000-01-01 |
dc.date.updated | 2018-10-24T05:25:32Z |
dc.audience.educationlevel | Màster |
dc.audience.mediator | Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística |
dc.audience.degree | MÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010) |