Course No.：S070103ZJ002
Course Category：Professional Basic Course
Period/Credits：40/2
Prerequisites：Advanced Probability.
Primary Coverage：
Continuous Martingales: Definitions; Maximal Inequalities; Convergence and Regularization Theorems; Optional Stopping Theorem; Brownian Motions.
Stochastic Integrals: Itô Integrals; Itô’s Formula; BDG’s Inequalities; Girsanov’s Theorem; Integral Representation of Martingales.
Stochastic Differential Equations: Definitions; Existence and Uniqueness of Solutions; Diffusion Process and Uniqueness in Law.
References：
[1] S.W. He, J.G. Wang and J.A. Yan，Semimartingale Theory and Stochastic Calculus，Academic Press of China, 1995. (in Chinese)
[2] Z.Y. Huang, Foundation of Stochastic Analysis, Academic Press of China，2nd ed., 2001. (in Chinese)
[3] I. Karatzas and S.E. Shreve, Brownian Motion and Stochastic Calculus, 2nd ed., Springer-Verlag, New York, 1991.
[4] D. Revuz and M. Yor, Continuous martingales and Brownian motion, Grund.Math.Wiss., 293, 3rd ed., Springer-Verlag, 1999.
Author：Guilan Cao (School of Mathematical Sciences, GUCAS)
Date：June, 2009
