Original title: Stochastické evoluční systémy a jejich aplikace
Translated title: Stochastic Evolution Systems and Their Applications
Authors: Rubín, Tomáš ; Maslowski, Bohdan (advisor) ; Hlubinka, Daniel (referee)
Document type: Master’s theses
Year: 2016
Language: eng
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
Keywords: analytic semigroups; C0-semigroups; cylindrical fractional Brownian motion; singular fractional Gaussian noise; stochastic evolution equations; analytické semigrupy; C0-semigrupy; cylindrický frakcionální Brownův pohyb; singulární frakcionální gaussovský šum; stochastické evoluční rovnice

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/74822

Permalink: http://www.nusl.cz/ntk/nusl-344193


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Master’s theses