Subjects(version: 944)
Stochastic Analysis - NMTP432
Title: Stochastická analýza Department of Probability and Mathematical Statistics (32-KPMS) Faculty of Mathematics and Physics from 2023 summer 8 summer s.:4/2, C+Ex [HT] unlimited unlimited no no taught Czech, English full-time full-time
Guarantor: RNDr. Petr Čoupek, Ph.D.doc. RNDr. Daniel Hlubinka, Ph.D.prof. RNDr. Bohdan Maslowski, DrSc. Pravděp. a statistika, ekonometrie a fin. mat.M Mgr. PMSEM Mgr. PMSE > Povinně volitelné Mathematics > Probability and Statistics NMSA405 NSTP153 NMTP521, NMTP551, NMTP561, NMTP562 NSTP168, NSTP149, NSTP153 NMTP533, NMTP543
 Annotation - ---CzechEnglish
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 - ---CzechEnglish
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 - ---CzechEnglish
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 - ---CzechEnglish
Last update: RNDr. Petr Čoupek, Ph.D. (16.02.2023)

Lecture and exercises.

 Requirements to the exam - ---CzechEnglish
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 - ---CzechEnglish
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 - ---CzechEnglish
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).

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