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Theory of Stochastic Evolution Equations (ThSDE)5 ECTS (englische Bezeichnung: Theory of Stochastic Evolution Equations)
(Prüfungsordnungsmodul: Theory of stochastic evolution equations)
Modulverantwortliche/r: Günther Grün Lehrende:
Günther Grün
Startsemester: |
SS 2018 | Dauer: |
1 Semester | Turnus: |
jährlich (WS) |
Präsenzzeit: |
113 Std. | Eigenstudium: |
37 Std. | Sprache: |
Englisch |
Lehrveranstaltungen:
Empfohlene Voraussetzungen:
Basic knowledge in probability theory or functional analysis is recommended.
Inhalt:
- Infinitely dimensional Wiener processes,
Stochastic integral in Hilbert spaces,
Ito-processes and stochastic differential equations,
Optionally: existence results for stochastic partial differential equations or further results on stochastic ODE (Fokker-Planck equations, . . .)
Lernziele und Kompetenzen:
Students
characterize Gaussian measures on Hilbert spaces. They explain representation formulas for Q-Wiener processes as well as the derivation of the stochastic integral,
successfully apply concepts to solve stochastic differential equations explicitly and prove existence of solutions to stochastic evolution equations.
Literatur:
- G. Da Prato & J. Zabczyk: Stochastic equations in infinite dimensions, Cambridge University Press
I. Karatzas & S.E. Shreve: Brownian motion and stochastic calculus, Springer
B. Oksendal: Stochastic differential equations, Springer
C. Prévôt & M. Röckner: A concise course on stochastic partial differential equations, Springer
Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:
- Computational and Applied Mathematics (Master of Science)
(Po-Vers. 2017w | NatFak | Computational and Applied Mathematics (Master of Science) | Specialisation:Modeling and applied analysis (MApA) and numerical analysis and simulation (NASi) | Theory of stochastic evolution equations)
- Computational and Applied Mathematics (Master of Science)
(Po-Vers. 2017w | NatFak | Computational and Applied Mathematics (Master of Science) | Specialisation: Modeling and applied analysis (MApA) and optimization (Opti) | Theory of stochastic evolution equations)
Dieses Modul ist daneben auch in den Studienfächern "Mathematik (Master of Science)", "Technomathematik (Master of Science)", "Wirtschaftsmathematik (Master of Science)" verwendbar. Details
Studien-/Prüfungsleistungen:
Theory of stochastic evolution equations (Prüfungsnummer: 59071)
(englischer Titel: Theory of stochastic evolution equations)
- Prüfungsleistung, mündliche Prüfung, Dauer (in Minuten): 15, benotet, 5.0 ECTS
- Anteil an der Berechnung der Modulnote: 100.0 %
- Erstablegung: SS 2018, 1. Wdh.: SS 2018
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