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Probability Theory 2 - NMSA405

Title:	Teorie pravděpodobnosti 2
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2015 to 2017
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	English, Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Zbyněk Pawlas, Ph.D.
Class:	M Mgr. PMSE M Mgr. PMSE > Povinné
Classification:	Mathematics > Probability and Statistics
Incompatibility :	NSTP051
Interchangeability :	NSTP051
Is pre-requisite for:	NMFM535, NMST450, NMTP434, NMTP436, NMTP432, NMTP450, NMTP438
Is interchangeable with:	NSTP145, NSTP051

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KPMS (15.05.2013)

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 (15.05.2013)

To explain basics of the martingale theory.

Literature - Czech

Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (28.10.2019)

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: RNDr. Jiří Dvořák, Ph.D. (28.09.2020)

Lecture+exercises.

Syllabus -

Last update: T_KPMS (24.04.2015)

1. random sequence, finite-dimensional distributions, Daniell's theorem

2. filtration, stopping times, martingale (submartingale, supermartingale) with discrete time

3. optional stopping and optional sampling theorem, maximal inequalities

4. convergence of submartingales

5. limit theorems for martingale differences