Syllabus
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
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.