Materials Covered in Math 562
In the following, [1] stands for the third edition of the book ``Continuous
martingales and Brownian motion'' by D. Revuz and M. Yor, and [2] stands
for the second edition of thebook ``Brownian motion and stochastic calculus''
by I. Karatzas and S. E. Shreve.
- Functions of finite variation and Stieltjes integral: [1] Section 0.4.
- Weak convergence in metric spaces: [1] Section 0.5 or
[2] Section 2.4.A.
- The space C[0, infinity): [2] Section 2.4.B, Section 2.4.C and
[2], pp 1-2.
- Brownian motion: [1], pp 17-21, [2], Section 2.1, Section 2.2,
Section 2.4.D
- Gaussian processes:Handout
- Sample path properties of Brownian motion: [1], 1.2.
- Filtrations and stopping times: [1], 1.4
- Martingales: [1], 2.1, 2.1, 2.3
- Markov processes: [1], 3.1, 3.1, 3.3
- Stochastic Integration: [1], 4.1, 4.2, 4.3, 4.4
- Representation of Martingales: [1], 5.1, 5.3
- Girsanov theorem: [2], 3.5
- SDE: [2], 5.2, 5.3, 5.4