Probability Theory - Alain-Sol Sznitman - 2017
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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. As I then mentioned the symmetric stable distribution with its characteristic function he wanted to know how we derived this characteristic function.
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.
Raffael, 07.02.2018, 11:00-11:30
Sznitman behaves exactly the way he is described in old protocols. He is rather unfriendly and not at all as happy as he acts during the lectures. My strategy was just to kind of ignore his picky comments and do as I was told (writing bigger, smaller, faster, right, left, whatever).
- Conditional expectation with shortly mentioning Radon-Nikodym
- Doob's inequality with proof (Attention: he is really picky about all the indices)
- Conditional expecation in the sense of orthogonal projection to the sub-Hilbertspace with proof
- Kolmogorov's Three Series Theorem with idea of the proof
- Lemmata of Borel Cantelli (idea of proof)
- convergence of stochastic series
All in all I guess the most important things is not to get intimidated by Sznitmans really radical style of examining. Small sidenote: When he says "put it in a box" he doesn't mean what he says but instead one should just draw a straigth line ^^
