σ-fields and Probability Spaces: Probability as a measure. Existence and uniqueness (Carathéodory theorem) of probability measures.
Independence: Sequences of events: 1st and 2nd Borel-Cantelli lemmas.
Random Variables: Measurable functions. Expectation of a random variable as Lebesgue integral. Characteristic function of a random variable.
Modes of Convergence: P. Lévy theorem.
Sums of Independent Random Variables: Strong Law of Large Numbers, Central Limit Theorem. Conditional expectation of a random variable.
Discrete Time Martingales.
- Teacher: Βασίλης Παπανικολάου
- Teacher: Σωτήριος Σαμπάνης
ECTS : 5
Language : el