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Measure Theoretic Probability
| Credits |
8 credit points |
| Instructors |
Kleijn, B.J.K. (Universiteit van Amsterdam), Spreij, P.J.C. (Universiteit van Amsterdam) |
| E-mail |
b.j.k.kleijn@uva.nl, spreij@science.uva.nl |
| Aim |
To provide an introduction in the basic notions and results of measure theory and how these are used in probability theory. |
| Description |
During the course the measure theoretic foundations of probability theory will be treated. Key words for the course are: measurable space, limit theorems for Lebesgue integrals, product measures, random variables, distributions of random variables, different convergence concepts for random variables (convergence in probability, weak convergence, convergence in p-th mean) and relations between them, uniform integrability, conditional expectation and conditional distribution. All these topics will be present in the treatment of martingale theory in discrete time. Finally, the existence of Brownian motion is proved. |
| Organization |
In most of the weeks there will be two hours of regular class and onehour filled by student presentations (which are a compulsary part of the programme). |
| Examination |
Homework exercises and exam. |
| Literature |
Lecture notes. |
| Prerequisites |
Knowledge at the level of for instance Richard T. Durrett, The Essentials of Probability and the first seven chapters of Walter Rudin, Principles of Mathematical Analysis. |
| Remarks |
Remarks Homepage of this course: http://staff.science.uva.nl/~spreij/onderwijs/master/mtp.html |
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