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 March 15th, 2012, 08:07 AM #1 Newbie   Joined: Mar 2012 Posts: 2 Thanks: 0 Summer school course in advanced prob. theory Dear all, I would like to take a course in advanced probability theory during the summer. I have searched for a University that offers courses in advanced probability theory but without luck... If any of you have any suggestions please let me know Best regards
 March 15th, 2012, 09:44 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Summer school course in advanced prob. theory What do you mean by advanced probability theory? Are we talking sigma-algebras and Kuratowski theorems, or more like kurtosis, cross-correlations, and convolutions? The first is what I think of as advanced probability, but perhaps you mean more of the second (advanced topics in probability, with some statistics, but less abstract the the former).
 March 15th, 2012, 02:33 PM #3 Newbie   Joined: Mar 2012 Posts: 2 Thanks: 0 Re: Summer school course in advanced prob. theory You are right. I should be more specific! I look for courses that cover some (not all) of the following topics: 1) Sigma-algebras: definition, properties, Borel-sigmaalgebra. 2) Measures: definition, properties, Lebesgue measure, probability measures. 3) Uniqueness theorem (without proof). Distribution functions. 4) Measurable functions: definition, properties, case-by-case result, stochastic variables. 5) Integral: construction, theorems on monotone and majorized convergence, relation to simpler concepts of the integral. 6) Functions, given as integrals: continuity, differentiability, interchanging of limit operations. 7) The function spaces L1 and L2: completeness. Mean and variance. 8) Measures with density. Probability densities. 9) Image measures. Transformation of probability measures. 10) The transformation theorem in 1 dimension. 11) Product measures: definition, the theorems of Tonelle and Fubini, independent stochastic variables. 12) Fouriertransformation (L1). 13) Sequence of random variables, almost sure convergence, Kolmogorov's 0-1 law. 14) The strong law of large numbers. 15) Weak convergence of probability measures. 16) The central limit theorem. 17) The ergodic theorem. Other topics from measure theory or stochastic processes (Brownian motion) would be nice too... I know it's a lot but I'm looking for a course that approximates a course covering the first 12 points. I need it to take some finance courses so all topics might not be neccesary.

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