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Stochastic Analysis - NMTP432

Title:	Stochastická analýza
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	summer
E-Credits:	8
Hours per week, examination:	summer s.:4/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	RNDr. Petr Čoupek, Ph.D. doc. RNDr. Daniel Hlubinka, Ph.D. prof. RNDr. Bohdan Maslowski, DrSc.
Class:	Pravděp. a statistika, ekonometrie a fin. mat. M Mgr. PMSE M Mgr. PMSE > Povinně volitelné
Classification:	Mathematics > Probability and Statistics
Pre-requisite :	NMSA405
Is incompatible with:	NSTP153
Is pre-requisite for:	NMTP521, NMTP551, NMTP561, NMTP562
Is interchangeable with:	NSTP168, NSTP149, NSTP153
In complex pre-requisite:	NMTP533, NMTP543

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

Last update: doc. Ing. Marek Omelka, Ph.D. (16.02.2023)

Lectures and exercises are devoted to stochastic processes with continuous time and to the basics of stochastic calculus.

Aim of the course -

Last update: RNDr. Petr Čoupek, Ph.D. (16.02.2023)

Students will broaden their knowledge about stochastic processes with continuous time and they will get acquainted with basics results of stochastic calculus.

Course completion requirements -

Last update: RNDr. Petr Čoupek, Ph.D. (16.02.2023)

Students need to obtain the credit for the exercise class and pass an exam. To take the exam, it is necessary to obtain the credit for the exercise class first. Students can obtain the credit for the exercise class by submitting their own sufficiently worked-out solutions of 3 homework problems by the specified deadlines. The nature of this condition prevents retry.

Literature - Czech

Last update: RNDr. Petr Čoupek, Ph.D. (16.02.2023)

[1] Karatzas, I., Shreve, D.E.: Brownian Motion and Stochastic Calculus. Springer, New York, ed. 2, 1998.

[2] Revuz, D., Yor, M.: Continuous Martingales and Brownian Motion, Springer-Verlag Berlin Heidelberg, ed. 3, 1999.

[3] Protter, P.E.: Stochastic Integration and Differential Equations, Spriner-Verlag Berlin Heidelberg, ed. 2, 2004.

[4] Le Gall, J.-F.: Brownian Motion, Martingales, and Stochastic Calculus, Springer Cham, ed. 1, 2016.

Teaching methods -

Last update: RNDr. Petr Čoupek, Ph.D. (16.02.2023)

Lecture and exercises.

Requirements to the exam -

Last update: RNDr. Petr Čoupek, Ph.D. (23.02.2023)

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. (23.02.2023)

1. Stochastic processes with continuous time

2. Wiener process

3. Filtrations and stopping times

4. Martingales with continuous time

5. Local martingales

6. Continuous semimartingales

7. Stochastic integral and Ito’s formula

8. Stochastic differential equations

Entry requirements -

Last update: RNDr. Petr Čoupek, Ph.D. (16.02.2023)

Basic knowledge of proability theory (modes of convergence for random variables, conditional expectation, etc.) and theory of stochastic processes (martingales with discrete time).