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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
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

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KPMS (09.05.2008)

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.

Aim of the course -

Last update: T_KPMS (09.05.2008)

To explain basics of the martingale theory.

Literature - Czech

Last update: T_KPMS (16.05.2011)

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

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

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

Teaching methods -

Last update: G_M (27.05.2008)

Lecture.

Syllabus -

Last update: T_KPMS (09.05.2008)

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