Course No.：S070103ZJ001
Course Category：Professional Basic Course
Period/Credits：40/2
Prerequisites：Advanced Probability.
Primary Coverage：
Introduction (Basic Concepts for Stochastic Processes, Existence of a Stochastic Process).
Discrete Martingales (Doob’s Convergence Theorem, Uniform Integrability, Sampling Theorem).
Markov Chains (Random Walk, Classification on the State Space of a Markov Chain, Ergodic Theory).
Lévy Process (Brownian Motion, Poisson Point Process, Stable Process, Surbordinator).
References：
[1] J. Bertoin, Lévy Processes, Cambridge Univ. Press, 1996.
[2] K.L. Chung, Markov Chains with Stationary Transition Probability, Springer-Verlag, 1960.
[3] D. Freedman, Brownian Motion and Diffusion, Springer-Verlag, 1971.
[4] D.H. Hu, Stochastic Processes, Wuhan Univ. Press, 2000 (In Chinese).
Author：Xiaoyu Hu (School of Mathematical Sciences, GUCAS)
Date：June, 2009
