M345P6 (Advanced) Probability Theory

Office Hours (Room: 6M55 )

M345P6&7 : Mo 15-16 , Tue 13:30-14:30

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.

MP6 Content 2018






Problem Sets

PS.1 ; PS.2 ; PS.3 ; PS.4 ; PS.5 ;

PS.1slns ; PS.2slns ; PS.3slns ; PS.4slns ;



Notes

notes.1 ; notes.2 ;






BIBLIOGRAPHY

Williams, D., Probability with Martingales.

Kolmogorov, A. N. Foundations of the theory of probability (+pdf)

Kac, Mark, Statistical Independence in Probability, Analysis and Number Theory.

Stroock, Daniel W., Probability Theory: An analytic view (Ch. I)

Leonid Koralov, Yakov G. Sinai, Theory of Probability and Random Processes(+pdf)

Sinai, Y.G., Probability theory : an introductory course (Google Books)

Schilling, Rene L., Measures, integrals and martingales

Stroock, Daniel W., Mathematics of Probability

Feller, William , An Introduction to Probability Theory and Its Applications,

Patrick Billingsley Probability and Measure (pdf)

Stroock, Daniel W., A concise introduction to the theory of integration







Some LINKS

Rademacher Functions, etc..


History of Mathematics :

A Simple Pole in Ithaca, NY” by Daniel W. Stroock

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)

Mathematicians:










Math Info

Vitali nonmeasurable set

M.G. Nadkarni and V.S. Sunder
Hamel bases and measurability

Gaussian Random Variables

Gibbs Random Fields




Mid-term lecture feedback questions