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Lecture 62: martingale representation theorem duration 27 minutes 42 seconds Lecture 62: martingale representation theorem Lecture 62: martingale representation theorem	Lecture 62: martingale representation theorem The martingale representation theorem in the case of a multidimensional Brownian motion: representation of L^2 martingales and local martingales. martingale representation theorem local martingale filtration generated by a stochastic process brownian motion girsanov theorem girsanov kernel From Tiziano Vargiolu 26 plays 0
Lecture 26: change of probability with a… duration 52 minutes 57 seconds Lecture 26: change of probability with a… Lecture 26: change of probability with a filtration	Lecture 26: change of probability with a filtration Equivalent probability measures. Conditional expectation and martingales under the new probability. absolutely continuous probabilities equivalent probabilities conditional expectation martingale property filtration density of probabilities density process From Tiziano Vargiolu 20 plays 0
Lecture 4: stochastic processes duration 22 minutes 56 seconds Lecture 4: stochastic processes Lecture 4: stochastic processes	Lecture 4: stochastic processes Filtration. Stochastic process. Stochastic process adapted to a filtration. Natural filtration of a stochastic process. Martingales, submartingales and supermartingales: definition and properties. filtration filtration generated by a stochastic process natural filtration of a stochastic process stochastic process stochastic process adapted to a filtration martingales supermartingale submartingale jensen inequality From Tiziano Vargiolu 26 plays 0