dc.contributor.advisor | Maslowski, Bohdan | |
dc.creator | Rubín, Tomáš | |
dc.date.accessioned | 2017-05-31T23:25:47Z | |
dc.date.available | 2017-05-31T23:25:47Z | |
dc.date.issued | 2016 | |
dc.identifier.uri | http://hdl.handle.net/20.500.11956/74822 | |
dc.description.abstract | In the Thesis, linear stochastic differential equations in a Hilbert space driven by a cylindrical fractional Brownian motion with the Hurst parameter in the interval H < 1/2 are considered. Under the conditions on the range of the diffusion coefficient, existence of the mild solution is proved together with measurability and continuity. Existence of a limiting distribution is shown for exponentially stable semigroups. The theory is modified for the case of analytical semigroups. In this case, the conditions for the diffusion coefficient are weakened. The scope of the theory is illustrated on the Heath-Jarrow-Morton model, the wave equation, and the heat equation. 1 | en_US |
dc.language | English | cs_CZ |
dc.language.iso | en_US | |
dc.publisher | Univerzita Karlova, Matematicko-fyzikální fakulta | cs_CZ |
dc.subject | stochastické evoluční rovnice | cs_CZ |
dc.subject | singulární frakcionální gaussovský šum | cs_CZ |
dc.subject | cylindrický frakcionální Brownův pohyb | cs_CZ |
dc.subject | C0-semigrupy | cs_CZ |
dc.subject | analytické semigrupy | cs_CZ |
dc.subject | stochastic evolution equations | en_US |
dc.subject | singular fractional Gaussian noise | en_US |
dc.subject | cylindrical fractional Brownian motion | en_US |
dc.subject | C0-semigroups | en_US |
dc.subject | analytic semigroups | en_US |
dc.title | Stochastic Evolution Systems and Their Applications | en_US |
dc.type | diplomová práce | cs_CZ |
dcterms.created | 2016 | |
dcterms.dateAccepted | 2016-06-09 | |
dc.description.department | Department of Probability and Mathematical Statistics | en_US |
dc.description.department | Katedra pravděpodobnosti a matematické statistiky | cs_CZ |
dc.description.faculty | Matematicko-fyzikální fakulta | cs_CZ |
dc.description.faculty | Faculty of Mathematics and Physics | en_US |
dc.identifier.repId | 141034 | |
dc.title.translated | Stochastické evoluční systémy a jejich aplikace | cs_CZ |
dc.contributor.referee | Hlubinka, Daniel | |
dc.identifier.aleph | 002092431 | |
thesis.degree.name | Mgr. | |
thesis.degree.level | navazující magisterské | cs_CZ |
thesis.degree.discipline | Pravděpodobnost, matematická statistika a ekonometrie | cs_CZ |
thesis.degree.discipline | Probability, mathematical statistics and econometrics | en_US |
thesis.degree.program | Matematika | cs_CZ |
thesis.degree.program | Mathematics | en_US |
uk.thesis.type | diplomová práce | cs_CZ |
uk.taxonomy.organization-cs | Matematicko-fyzikální fakulta::Katedra pravděpodobnosti a matematické statistiky | cs_CZ |
uk.taxonomy.organization-en | Faculty of Mathematics and Physics::Department of Probability and Mathematical Statistics | en_US |
uk.faculty-name.cs | Matematicko-fyzikální fakulta | cs_CZ |
uk.faculty-name.en | Faculty of Mathematics and Physics | en_US |
uk.faculty-abbr.cs | MFF | cs_CZ |
uk.degree-discipline.cs | Pravděpodobnost, matematická statistika a ekonometrie | cs_CZ |
uk.degree-discipline.en | Probability, mathematical statistics and econometrics | en_US |
uk.degree-program.cs | Matematika | cs_CZ |
uk.degree-program.en | Mathematics | en_US |
thesis.grade.cs | Výborně | cs_CZ |
thesis.grade.en | Excellent | en_US |
uk.abstract.en | In the Thesis, linear stochastic differential equations in a Hilbert space driven by a cylindrical fractional Brownian motion with the Hurst parameter in the interval H < 1/2 are considered. Under the conditions on the range of the diffusion coefficient, existence of the mild solution is proved together with measurability and continuity. Existence of a limiting distribution is shown for exponentially stable semigroups. The theory is modified for the case of analytical semigroups. In this case, the conditions for the diffusion coefficient are weakened. The scope of the theory is illustrated on the Heath-Jarrow-Morton model, the wave equation, and the heat equation. 1 | en_US |
uk.file-availability | V | |
uk.publication.place | Praha | cs_CZ |
uk.grantor | Univerzita Karlova, Matematicko-fyzikální fakulta, Katedra pravděpodobnosti a matematické statistiky | cs_CZ |
dc.identifier.lisID | 990020924310106986 | |