STAT 437: Probability

STAT 437	CRN 8112, 15 Points (2009 1/3)
Coordinator:	Prof Estate Khmaladze
Prerequisites:	STAT 333; (MATH 301 or MATH 312 recommended).
Lectures:	Wed 4-6 timetable
Recommended Reading:	S. Ross, Stochastic Processes, 2nd ed., Wiley; Feller, An Introduction to Probability Theory and its Applications (Vol 1); A.N. Shiryaev, Probability, 2nd ed., Springer.
Description:	Probability spaces and convergences: almost sure, in probability, L_p-convergences, weak convergence of probability measures. [The question of how random sequences converge and to what has very diverse and interesting answers in probability theory.] Central Limit Problem: infinitely divisible distributions and Levy-Khinchine representation,with examples, Lindeberg CLT, non-classical CLT (without asymptotic negligibility). [Gaussian random variable is typically viewed as a limit of a sum of "small" independent summands. However, "small" these summands can be in a huge variety of ways, and, as the result, we have a huge class of limit distributions, very different from Gaussian.] Stable distributions, with real life examples form finance. Levy processes and elements of weak convergence. Applications to modeling phenomena in finance, physiology and earth science.