office: MSB M222
office hours:   TTH 10:45-12:15 (to be changed in January)
N. V. Krylov
Introduction to the theory of random processes
Graduate Studies in Mathematics, 43. AMS 2002.
This course is the second part of the one year graduate course in probability theory. The course requires a basic understanding of the material of Math 322. The course will include: general facts about random processes, probabilities on Polish spaces, weak convergence and tightness, Brownian motion, Markov and strong Markov properties, continuous time martingales, Ito stochastic integral, Girsanov's theorem, stationary processes and their spectral representation, Gaussian processes, Levy processes, Gibbs measures and diffusions on fractals.