M3P6 (Advanced) Probability Theory

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.

Problem Sets

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



Williams, D., Probability with Martingales.

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

Sinai, Y.G., Probability theory : an introductory course

Schilling, Rene L., Measures, integrals and martingales

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

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

Feller, William , An Introduction to Probability Theory and Its Applications, (vol I) (vol II)

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



Rademacher Functions, etc..

History of Mathematics :
Petersburg Game :