Brownian Motion and Stochastic Calculus - Pierre Nolin - 2016

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17.08.2016, 9.30 Uhr, jerni

General about the exam: The exam takes place at the blackboard; prof. Nolin asks the questions which seem to be prepared on his paper. He and also an assistant - in my exam Avelio Sepulveda - take notes. The assistant didn't interact with me. Topics: It started very basic, asking the definition of a BM and then going to the \( (G_t)-BM \) and P. Lévy's characterization of it. He didn't ask for a proof of this one. Then we talked about the construction of stochastic integrals and I started step by step with basic process, then simple processes going on up to \( \Lambda_3 \). He asked some details where he wasn't satisfied with the information I provided, but overall he didn't ask for detailed proofs. Then we switched the topic and talked about harmonic functions. He wanted to see a definition and then asked for an application in our lecture. I mentioned "BM doesn't hit points when d>1" and then we did a quite detailed proof of this one, including the use of Ito's formula ond so on. After this, the time was over. All in all not a stressful exam with an enjoyful atmosphere and a very kind professor.