Advanced Probability (I)
- Filtered Probability Space, filtration and stochastic processes adapted to a filtration, natural filtration.
- Absolutely continuity and density of a measure with respect to another measure. Radon-Nikodym theorem, Definition of conditional probability with respect to a sigma field: existence and uniqueness with probability one
- Properties of conditional probability with respect to a sigma field. Definition and properties of conditional expectation with respect to a sigma field. Definition and properties of martingale and sub martingale with respect to filteration