MATH 519 - Stochastic Processes - FALL 2009

The course will give a comprehensive introduction to a modern topic in stochastic analysis and stochastic processes: Levy Processes and Stochastic Calculus with application to Financial Mathematics and Stochastic Differential Equations. The course is a continuation of last semester's course by A. Novikov, but that course is not a prerequisite. I am planning to begin with an overview of basic probabilty notions (e.g. martingales, stochastic process...). The lecture will cover: infinitely divisible laws, stable distributions, Levy processes, semigroups and generators of Markov processes, stochastic integration (multiple integrals), Malliavin calculus, mathematical finance, stochastic differential equations.