Theory of Probability III (MATH 230C)

3 credits · Graduate

Continuous time stochastic processes: martingales, Brownian motion, stationary independent increments, Markov jump processes and Gaussian processes. Invariance principle, random walks, LIL and functional CLT. Markov and strong Markov property. Infinitely divisible laws. Some ergodic theory. Prerequisites for UG and masters students: Math 230B / Stats 310B