M345P6 (Advanced) Probability Theory
Lectures Spring 2020
Mo 13:00 – 15:00/ HXLY 144 / & Thu 10:00 - 11:00 / HXLY 213 Clore ( First week only HXLY 139 ) /
Office Hours (Room: 6M55 )
M345P6 Tue 12:00-13:00
Syllabus A rigorous approach to the fundamental properties of probability: Probability measures. Random variables. Independence. Sums of independent random variables; Weak and Strong Laws of Large Numbers. Weak convergence, characteristic functions, Central Limit Theorem. Elements of Brownian motion. Ergodic Theory.
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Problem Sets PS.1 ; PS.2 ; PS.3 ; PS.4 ; PS.5 ; PS.1slns ; PS.2slns ; PS.3slns ; PS.4slns ; PS.5slns ; Course Work |
Notes Content 2020 : |
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BIBLIOGRAPHY Leonid Koralov, Yakov G. Sinai, Theory of Probability and Random Processes(+pdf) Sinai, Y.G., Probability theory : an introductory course (Google Books) Imperial College Library Electronic Resources
Kolmogorov, A. N. Foundations of the theory of probability (+pdf) Kac, Mark, Statistical Independence in Probability, Analysis and Number Theory. Patrick Billingsley Probability and Measure (pdf) Stroock, Daniel W., Probability Theory: An analytic view (Ch. I) Schilling, Rene L., Measures, integrals and martingales Stroock, Daniel W., Mathematics of Probability Feller, William , An Introduction to Probability Theory and Its Applications, Williams, D., Probability with Martingales. Stroock, Daniel W., A concise introduction to the theory of integration |
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Some LINKS “A Simple Pole in Ithaca, NY” by Daniel W. Stroock Mark Kac at St-Andrews Math History Théorie analytique des probabilités; by Laplace, Pierre Simon, marquis de, 1749-1827 (http://sites.mathdoc.fr/cgi-bin/oeitem?id=OE_LAPLACE__7_R2_0) Özlem Kart, A Historical Survey of the Development of Classical Probability Theory
Glenn Shafer & Vladimir Vovk The origins and legacy of Kolmogorov’s Grundbegriffe Mathematicians:
Mikhail Lifshits, Lectures on Gaussian Processes
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Math Info M.G. Nadkarni and V.S. Sunder Hamel bases and measurability Fundamentals of Stein’s method∗Nathan Ross
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Mid-term lecture feedback questions