Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 236A: Stochastic Dynamics and Applications
Approved: 2009-03-01, Albert Fannjiang

Units/Lecture:

Fall, alternate years; 4 units; lecture/term paper or discussion

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
B. Oksendal, Stochastic Differential Equations, ($50)
Search by ISBN on Amazon: 038715292X

Prerequisites:

MAT/STA 235B, or consent of instructor. A working knowledge of the material in the entire probability sequence MAT/STA 235ABC is recommended. MAT/STA 235AB may be taken concurrently.

Course Description:

Stochastic processes, Brownian motion, Stochastic integration, martingales, stochastic differential equations. Diffusions, connections with partial differential equations, mathematical finance.

Suggested Schedule:

Department Syllabus
MAT 236A: Stochastic Dynamics and Applications

When taught: Fall, alternate years
Suggested text ($): B. Oksendal, Stochastic Differential Equations, ISBN-10: 038715292X ($50)
Units/lectures: 4 units; lecture/term paper or discussion
Prerequisites: MAT/STA 235
Lectures Sections Topics/Comments
1 1.1 - 1.6 Motivation, examples
1 2.1 - 2.2 Review: probability space, stochastic processes
3 3.1 - 3.3 Ito integrals, chaos expansion
2 4.1 - 4.2 Ito formula: 1-d, multi-d
1 4.3 Martingale representation theorem
1 5.1 Examples and solution methods for SDE's
1 5.2 Existence and uniqueness
1 5.3 Weak and strong solutions
2 7.1 - 7.2 Diffusions: Markov property
2 7.3 - 7.4 Generator, Dynkin formula
1 8.1 Kolmogorov's backward equations
1 8.2 Feynman-Kac formula
1 8.3 Martingale problem
2 8.5 Random time change
2 8.6 Girsanov theorem
2 9.1 - 9.3 Dirchlet problem, Poisson problem
2 6.1 - 6.3 Linear filtering
2 10.1 - 10.4 Optimal stopping (shortened and simplified)