Stochastic Analysis

  • 申立勇
  • Created: 2014-12-08
Stochastic Analysis


Course No.S070103ZJ002

Course CategoryProfessional Basic Course


PrerequisitesAdvanced 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.


[1] S.W. He, J.G. Wang and J.A. YanSemimartingale Theory and Stochastic CalculusAcademic Press of China, 1995. (in Chinese)

[2] Z.Y. Huang, Foundation of Stochastic Analysis, Academic Press of China2nd 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.

AuthorGuilan Cao (School of Mathematical Sciences, GUCAS)

DateJune, 2009