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Malliavin Calculus - NMTP561

Title:	Malliavinův počet
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, Czech
Teaching methods:	full-time
Teaching methods:	full-time
Note:	the course is taught as cyclical

Guarantor:	RNDr. Petr Čoupek, Ph.D.
Class:	Pravděp. a statistika, ekonometrie a fin. mat. M Mgr. PMSE M Mgr. PMSE > Volitelné
Classification:	Mathematics > Probability and Statistics
Pre-requisite :	NMTP432

Annotation -

Last update: doc. Ing. Marek Omelka, Ph.D. (30.11.2020)

The lecture presents basic notions and applications of Malliavin calculus.

Aim of the course -

Last update: RNDr. Petr Čoupek, Ph.D. (03.12.2020)

Students will get acquainted with basic results of Mallivin calculus.

Course completion requirements -

Last update: RNDr. Petr Čoupek, Ph.D. (03.12.2020)

Students need to pass an oral exam.

Literature -

Last update: RNDr. Petr Čoupek, Ph.D. (03.12.2020)

[1] Nualart, D., Nualart, E. Introduction to Malliavin Calculus, Cambridge University Press, 2018.

[2] Nualart, D. The Malliavin calculus and related topics, Springer-Verlag Berlin/Heidelberg, 2006.

[3] Nourdin, I., Peccati, G. Normal approximations with Malliavin calculus: From Stein’s method to universality, Cambridge University Press, 2012.

Teaching methods -

Last update: RNDr. Petr Čoupek, Ph.D. (03.12.2020)

Lecture.

Requirements to the exam -

Last update: RNDr. Petr Čoupek, Ph.D. (03.12.2020)

The exam is oral; the requirements correspond to the syllabus of the course to the extent in which it was presented during the lectures.

Syllabus -

Last update: RNDr. Petr Čoupek, Ph.D. (03.12.2020)

1. Isonormal Gaussian process.

2. Wiener chaos and multiple integrals.

3. Malliavin derivative and its adjoint.

4. Ornstein-Uhlenbeck semigroup.

5. Applications.

Entry requirements -

Last update: RNDr. Petr Čoupek, Ph.D. (03.12.2020)

Basic knowledge of stochastic analysis (Wiener process, stochastic integral) and functional analysis (Hilbert and Banach space, linear operator).