Probability Theory - Alain-Sol Sznitman - 2017
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Contents
Marc, 05.02.2018, 15:30-16:00
- Doob's decomposition with proof
- Doob's inequality with proof (he wanted me to explain properly why \((H\cdot X)_{n}=X_{n}-X_{T\wedge n}, n \geq 0\)).
- Definition of the characteristic function.
- State some properties of the characteristic function (without proving them).
- State the continuity theorem (without proof).
- Give two applications of the continuity theorem we had in the lecture.
In general, he wants you to state the theorems and definitions very precisely, i.e. you always have to indicate whether \(n \geq 1\) or \(n \geq 0\) for sequences of random variables, martingales etc. Otherwise he will interrupt you directly or later during the proof, when something goes wrong with the sets or random variables you defined on the blackboard.
