Probability Theory 2 - NSTP051
Title: Teorie pravděpodobnosti 2
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Guarantor: prof. RNDr. Viktor Beneš, DrSc.
Mgr. Petr Dostál, Ph.D.
Class: DS, ekonometrie a operační výzkum
Classification: Mathematics > Probability and Statistics
Co-requisite : NSTP050
Interchangeability : NMSA405
Is co-requisite for: NSTP145
Is incompatible with: NSTP032
Is pre-requisite for: NSTP119
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Annotation -
We start with the notions of sub-, super-, martingale. The lecture is mainly devoted to discrete time martingales. The detailed technical explanation serves as basics for extended courses, e.g. for stochastic analysis.
Last update: T_KPMS (09.05.2008)
Aim of the course -

To explain basics of the martingale theory.

Last update: T_KPMS (09.05.2008)
Literature - Czech

Štěpán J.: Teorie pravděpodobnosti. Matematické základy. Academia, Praha, 1987

Kallenberg, O.: Foundations of modern probability. Springer, 1997.

Lachout, P.: Diskrétní martingaly. Karolinum, Praha, 2007.

Last update: T_KPMS (16.05.2011)
Teaching methods -

Lecture.

Last update: G_M (27.05.2008)
Syllabus -

Martingales with discrete time, compensator, stopping time, optional stopping, optional sampling theorem, maximal inequalities, convergence of submartingales, central limit theorem for martingale differences.

Last update: T_KPMS (09.05.2008)