Theory of Stochastic Evolution Equations (ThSDE)5 ECTS
(englische Bezeichnung: Theory of Stochastic Evolution Equations)

Lectures:

• • Theory of Stochastic Evolution Equations
    (Vorlesung, 2 SWS, Günther Grün, Thu, 8:00 - 10:00, H5)
  • Übung zu Theory of Stochastic Evolution Equations
    (Übung, 0,5 SWS, Günther Grün)

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:
Das Modul ist im Kontext der folgenden Studienfächer/Vertiefungsrichtungen verwendbar:

1. 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)
2. 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)

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

1. Prüfer:

Günther Grün