Difference between revisions of "Probability Theory - Alain-Sol Sznitman - 2017"
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* State some properties of the characteristic function (without proving them). | * State some properties of the characteristic function (without proving them). | ||
* State the continuity theorem (without proof). | * State the continuity theorem (without proof). | ||
| − | * Give two applications of the continuity theorem we had in the lecture. | + | * 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. Then, finally, time was over. |
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. | 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. | ||
Revision as of 22:23, 5 February 2018
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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. As I then mentioned the symmetric stable distribution with its characteristic function he wanted to know how we derived this characteristic function. Then, finally, time was over.
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.
