Stochastic Differential Equations course, Spring 2012
The course homepage is here.
The course and most of the problems are based on Bernt Oksendal: Stochastic differential equations (6th edition), Springer, 2005.
Problem set No 1: Brownian motion. HW problems: 5, 6, 7, 8. Deadline: Feb 28 Tue.
Problem set No 2: Definition of Ito integral. HW problems: 2, 3(d), 4, 5. Deadline: March 13 Tue.
Problem set No 3: Ito's formula, martingale representation. HW problems: 2(b), 4(c), 5, 7, 8(b), 9(a). Deadline: March 20 Tue.
Problem set No 4: SDE's. (I have moved the problems on generators to the next set.) HW problems: 1(c), 4(b), 5. Deadline: March 27 Tue.
Problem set No 5: Generators of Ito diffusions, Dynkin's formula, Kolmogorov's backward equation, contraction semigroups. HW problems: 3, 6. Deadline: Apr 10 Tue.
Problem set No 6: More on contraction semigroups. Feynman-Kac formula. HW problems: 1(b), 2, 4. Deadline: May 3 Thu.
Problem set No 7: Radon-Nikodym martingales, Girsanov's theorem. HW problems: 4(b), 7. Deadline: May 10 Thu.