Module Handbook

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Module MAT-64-12-M-7

Malliavin Calculus and Applications (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-64-12-M-7 Malliavin Calculus and Applications 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-64-12-K-7
Malliavin Calculus and Applications
P 42 h 93 h - - PL1 4.5 irreg.
  • About [MAT-64-12-K-7]: Title: "Malliavin Calculus and Applications"; 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: 86283 ("Malliavin Calculus and Applications")

Evaluation of grades

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


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.

Competencies / intended learning achievements

Upon successful completion of this module, the students have gained basic knowledge of the Malliavin calculus and its applications. They are able to name the main propositions of the lecture, classify and explain the illustrated connections. They understand the proofs and are able to reproduce and explain them. In particular, they can critically assess, what conditions are necessary for the validity of the statements.

By solving the given exercise problems, they have gained a precise and independent handling of the terms, propositions and methods of the lecture. In addition, they have learned to apply the methods to new problems, analyze them and develop solution strategies.

Literature

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

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-64-12-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.)