Markov folyamatok és martingálok

1. Sigma algebras, conditional expectation and its properties
2. Martingales, stopped martingales, Doob's optional stopping theorem, applications (ABRACADABRA problem, hitting time for simple random walk)
3. Martingale convergence theorem, L² martingales, Doob decomposition, angle bracket process
4. Uniformly integrable martingales, Levy's upward and downward theorems, applications (Kolmogorov's 0-1 law, strong law of large numbers)
5. Doob's inequalities (submartingale inequality, L^p inequality), law of iterated logarithm