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Measure Theoretic Probability (STAR)
| Credits | 8 credit points |
| Instructors | Pistorius, M.R. (Universiteit van Amsterdam), van Zanten , J.H. (Universiteit van Amsterdam) |
| m.r.pistorius@uva.nl, j.h.vanzanten@uva.nl | |
| Aim | To provide an introduction to 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: limit theorems for Lebesgue integrals, product measures, random variables, distributions of random variables, convergence in probability, weak convergence, uniform integrability, conditional expectation, martingales in discrete time, convergence theorems for martingales, characteristic functions, central limit theorems. The course provides the necessary background for follow up courses like Stochastic Processes and Stochastic Integration, where in particular convergence theorems for martingales and characteristic functions are frequently used. |
| Organization | Knowlegde 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 |
| Examination | Written examination (E) and homework assignments (H). The final mark (F) is determined as F = max(E, 1/3 * H + 2/3 * E). |
| Prerequisites | The course is based on this set of lecture notes written by Peter Spreij. Lecturer: Martijn Pistorius Coordinator: Peter Spreij Tutor: Naser M.Asghari |
| Remarks | Please find more information on the website: |