Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-71-12-K-7

White Noise Analysis (4V+2U, 9.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 9.0 CP 186 h
4 V Lecture 56 h
2 U Exercise class (in small groups) 28 h
(4V+2U) 9.0 CP 84 h 186 h

Basedata

SWS 4V+2U
CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-SPAS] Analysis and Stochastics
Additional informations
Livecycle-State [NORM] Active

Contents

  • introduction to the basics of distribution theory with specific focus on tempered distributions,
  • construction of the White Noise space (Minlos theorem, chaos decomposition, T-transform, S-transform, Ito-Wiener-Segal isomorphism),
  • introduction of test function spaces and spaces of generalised functions of White Noise Analysis (Hida and Kondratiev spaces),
  • applications to Feynman path integrals and stochastic PDE.

Literature

  • T. Hida, H. H. Kuo, J. Potthoff, L. Streit: White Noise. An Infinite Dimensional Calculus,
  • N. Obata: White Noise Calculus and Fock Space,
  • H. H. Kuo: White Noise Distribution Theory,
  • B. Simon: Functional Integration and Quantum Physics,
  • Y.M. Berezansky and Y.G. Kondratiev: Spectral Methods in Infinite Dimensional Analysis.

Materials

Further literature will be announced in the lecture; Exercise material is provided.

Registration

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

Requirements for attendance (informal)

Knowledge from the module [MAT-70-11-M-4] Functional Analysis is useful, but not necessarily required.

Modules:

Courses

Requirements for attendance (formal)

None

References to Course [MAT-71-12-K-7]

Module Name Context
[MAT-71-12-M-7] White Noise Analysis P: Obligatory 4V+2U, 9.0 LP