Stochastic Evolution Systems and Their Applications
Stochastické evoluční systémy a jejich aplikace
diploma thesis (DEFENDED)
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http://hdl.handle.net/20.500.11956/74822Identifiers
Study Information System: 141034
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- Kvalifikační práce [11325]
Faculty / Institute
Faculty of Mathematics and Physics
Discipline
Probability, mathematical statistics and econometrics
Department
Department of Probability and Mathematical Statistics
Date of defense
9. 6. 2016
Publisher
Univerzita Karlova, Matematicko-fyzikální fakultaLanguage
English
Grade
Excellent
Keywords (Czech)
stochastické evoluční rovnice, singulární frakcionální gaussovský šum, cylindrický frakcionální Brownův pohyb, C0-semigrupy, analytické semigrupyKeywords (English)
stochastic evolution equations, singular fractional Gaussian noise, cylindrical fractional Brownian motion, C0-semigroups, analytic semigroupsIn 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