SUBJECT
Title
Discrete parameter martingales
Type of instruction
lecture
Level
master
Faculty
Part of degree program
Credits
2
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
- 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.
Readings
- Y. S. Chow – H. Teicher: Probability Theory – Independence, Interchangeability, Martingales. Springer, New York, 1978.
- J. Neveu: Discrete-Parameter Martingales. North-Holland, Amsterdam, 1975.