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.






 


BIBLIOGRAPHY

Williams, D., Probability with Martingales.

Kolmogorov, A. N. Foundations of the theory of probability

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

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

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



SOME FACTS AND EXAMPLES

Measure&Integration M3P2

MORE & AROUND

 

Some LINKS

Links


History of Mathematics :
Petersburg Game :

General Refs

World of MATH

Wikipedia

(Old M34P6 web page)