Difference between revisions of "Brownian Motion and Stochastic Calculus - 2018"
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| − | + | In the preparation room, I was given a piece of paper with two (handwritten) questions on it. The first told me to state and prove Blumenthal's 0-1-Law, and give it's consequences, in particular for regularity of boundary, etc. | |
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| + | The second question was a function of \(B_t\) and \(t\), use Ito to show that this is indeed a local martingale (straightforward, just calculate). | ||
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| + | In the exam, I first answered these question (here Werner did not say very much, just listened to what I had to say). After this was done, he asked some other questions. These included Brownian Bridge (definition, what do we use it for, covariance function, independence from \(B_1\)), and then the Fourier decomposition of Brownian motion, and the law of the coefficients (I first spoke about the \(L^2\)-decomposition and how this relates to Brownian motion, and concluded in the special case (Fourier basis is an \(L^2\)-basis). | ||
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| + | Werner is as always very relaxed, and created a really nice atmosphere during the exam. | ||
Revision as of 07:51, 7 August 2018
Please sign with your name and the date on which you had your exam. If you use this wiki, contribute to it as well or terrible things will happen to you: like me kicking you with my fists.
Nicholas Dykeman, 07.08.2018, 7:20-8:00
In the preparation room, I was given a piece of paper with two (handwritten) questions on it. The first told me to state and prove Blumenthal's 0-1-Law, and give it's consequences, in particular for regularity of boundary, etc.
The second question was a function of \(B_t\) and \(t\), use Ito to show that this is indeed a local martingale (straightforward, just calculate).
In the exam, I first answered these question (here Werner did not say very much, just listened to what I had to say). After this was done, he asked some other questions. These included Brownian Bridge (definition, what do we use it for, covariance function, independence from \(B_1\)), and then the Fourier decomposition of Brownian motion, and the law of the coefficients (I first spoke about the \(L^2\)-decomposition and how this relates to Brownian motion, and concluded in the special case (Fourier basis is an \(L^2\)-basis).
Werner is as always very relaxed, and created a really nice atmosphere during the exam.
