Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-64-12-K-7

Malliavin Calculus and Applications (2V+1U, 4.5 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 4.5 CP 93 h
2 V Lecture 28 h
1 U Exercise class (in small groups) 14 h
(2V+1U) 4.5 CP 42 h 93 h

Basedata

SWS 2V+1U
CP, Effort 4.5 CP = 135 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
Livecycle-State [NORM] Active

Contents

Fundamentals of Malliavin calculus:
  • Wiener chaos decomposition,
  • Malliavin derivative,
  • divergence operator and stochastic integration.

Applications:

  • regularity of probability measures,
  • anticipative stochastic differential equations,
  • Malliavin calculus in financial mathematics,
  • limit theorems.

Literature

  • D. Nualart: The Malliavin Calculus and Related Topics,
  • D. Nualart: Malliavin Calculus and Its Applications.

Materials

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

Requirements for attendance (informal)

Knowledge in Stochastic Analysis (e.g. from the module [[MISSING TEXT]] 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 Course [MAT-64-12-K-7]

Module Name Context
[MAT-64-12-M-7] Malliavin Calculus and Applications P: Obligatory 2V+1U, 4.5 LP