Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-64-13-M-7

Introduction to Stochastic Partial Differential Equations (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-64-13-M-7 Introduction to Stochastic Partial Differential Equations 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-SPAS] Analysis and Stochastics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V+1U MAT-64-13-K-7
Introduction to Stochastic PDE
P 42 h 93 h - - PL1 4.5 irreg.
  • About [MAT-64-13-K-7]: Title: "Introduction to Stochastic PDE"; Presence-Time: 42 h; Self-Study: 93 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: irregular (by arrangement)
  • Examination number: 86416 ("Introduction to Stochastic Partial Differential Equations")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

  • infinite-dimensional Wiener processes,
  • integration for operator-valued processes,
  • mild solutions of stochastic PDE (semigroup approach),
  • approximation methods.

Competencies / intended learning achievements

Upon successful completion of this module, the students have gained in-depth knowledge of important aspects (modelling, solution and regularity theory, approximation) of a subfield of Stochastic Analysis. They are able to name the essential propositions of the lecture as well as to classify and to explain the connections. They understand the proofs presented in the lecture and are able to reproduce and explain them.

By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies.

Literature

  • C. Prevot, M. Röckner: A Concise Course on Stochastic Partial Differential Equations,
  • G. Da Prato, J. Zabczyk: Stochastic Equations in Infinite Dimensions.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance (informal)

Knowledge in Stochastic Analysis (e.g. from the module [MAT-64-11-M-7] or [MAT-61-11-M-7]) and in Functional Analysis (e.g. from the module [MAT-70-11-M-4]).

Modules:

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-64-13-M-7]

Module-Pool Name
[MAT-70-MPOOL-7] Specialisation Stochastic Analysis (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)