Course for international guest/part time students

Faculty

Faculty of Science

Organization

TTK Department of Probability Theory and Statistics

Code

dipama1u0um17em

Title

Discrete parameter martingales (l)

Usual semester

Autumn

ECTS

3

Language

hu

Learning outcomes

Knowledge: Knowledge of basic concepts, results and methods in the field. Ability: Application of knowledge in the field, understanding of interrelationships and problem solving. Attitude: Desire to improve mathematical knowledge and to learn as much as possible, and to apply knowledge as widely as possible. Autonomy and responsibility: Formulate and analyse mathematical questions independently and evaluate the limits of their applicability responsibly.

Course content

Almost sure convergence of martingales. Convergence in Lp, regular martingales. Regular stopping times, Wald’s theorem. Convergence set of square integrable martingales. Hilbert space valued martingales. Central limit theory for martingales. Reversed martingales, U-statistics, interchangeability. Applications: martingales in finance; the Conway algorithm; optimal strategies in favourable games; branching processes with two types of individuals. Necessary prior knowledge: BSc level probability theory

Assessment method

lecture notes

Bibliography

oral exam

Recommended bibliography

Y. S. Chow – H. Teicher: Probability Theory – Independence, Interchangeability, Martingales. Springer, New York, 1978. J. Neveu: Discrete-Parameter Martingales. North-Holland, Amsterdam, 1975.

Programmes of the course