syll.prob - Syllabus for Probability MAP6472 5026 Jonathan...

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Unformatted text preview: Syllabus for Probability MAP6472 5026 Jonathan L.F. King University of Florida, Gainesville FL 32611-2082, USA [email protected] Webpage ∼ squash/ 4 May, 2010 (at 22:15 ) This is a full-year course that covers absolutely lovely mathematics. We’ll use Breiman’s fine book Probability , a classic now published by SIAM. What little measure theory we’ll need, I will develop in class. Topics include: The Weak and Strong Laws of Large Numbers; Independence (Kolmogorov zero-one law, Hewitt-Savage zero-one law etc); Conditional proba- bility; Martingales; and an initial foray into Markov Chains. If time permits, we’ll cover the basic Ergodic the- orems, depending on the interests of the students. I am open to special ( elementary ) topics, if a student has a particular need/interest. In the second semester, among other topics we’ll explore deeper into Markov chains, examine Brown- ian motion, and explore some probabilistic methods in Ergodic theory. In the second semester I am quitein Ergodic theory....
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  • Fall '11
  • King
  • Probability theory, Little Hall, Prof. JLF King, Kolmogorov zero-one law, Jonathan L.F. King, Hewitt-Savage zero-one law

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