Rice University
Instructors
Dennis CoxTime and Place
Duncan Hall 2080, 713 / 348 6007
Office Hours: T Th 10:50 - 12:00, or by appointment
Dr. Rudolf Riedi
Duncan Hall 2082, 713 / 348 3020,
Office Hours: TBA, or by appointment
Tuesday Thursday 9:25 - 10:40 am, Location DH 1042
Outline (to be refined as the course develops)
Grading
2/3 Homework
1/3 Test or Course Project [agree with instructor on project topic by March 12]
[Outline] [Textbooks] [Grading] [Reading] [Homework problems and solutions]
Material covered during class
This doubles as a calendar for the course.
Covered material | Suggested reading | |
January 13 | Orientation, history | |
January 15 |
review Measure theory | Lecture notes Cox or Kurtz |
January 20 |
continuity of Brownian motion,
filtration, martingales |
"Adventures..." (Resnick) for
construction of BM |
January 22 |
Langevin; Einstein: original
approaches to SDEs |
Oksendal Ch 1+2 |
January 27 |
White noise as a degenerate
process, stoch integral with deterministic integrand |
|
January 29 |
Ornstein-Uhlenbeck,
interpretation of SDEs, informal definition of Ito and Stratanovitch
integrals |
Oksendal Ch 1+2 |
February 3 |
Explicit computation of \int W dW |
Oksendal Ch 3 (p 28) |
February 5 | Adapted, mean square processes;
approximation by simple functions |
Oksendal Ch 3 (first half) |
February 10 | simple Ito Isometry; def of Ito integral; first extension | Oksendal Ch 3 (second half) |
February 12 | Ito Isometry; first properties
of Ito integral |
|
February 17 | Doob's martingale inequal;
continuity of integral |
|
February 19 | cancelled |
|
February 24 |
Ito formula; integration by parts |
Oksendal Ch 4 |
March 9 |
Examples of Solutions to SDE-s of solutions to SDE-s |
Oksendal 5.1 |
March 16 |
Existence and Uniqueness of solutions to SDE-s |
Oksendal 5.2 |
March 18 |
Weak and Strong Solutions of SDE, Time homogeneous Diffusions, Markov property |
Oksendal 5.3 Oksendal 7.1 |
March 23, 25, 30 |
Generator (dual, acting on
measures) |
|
April 1 |
Generator (acting on functions), Dynkin's formula, escape time from circle |
Oksendal 7.2+3 |
April 6, 8 |
Poisson approximation of
diffusion |
|
April 13 |
Kolmogorov backwards equation, Feynman-Kac equation |
Oksendal 8.1 |
April 15 |
Black-Scholes equation, Chemical system (Project) |
Oksendal 12 |
[Outline] [Textbooks] [Grading] [Reading] [Homework problems and solutions]
Homework
(tex-source and solutions restricted to Rice University)
Homework sheet | Due date (in class) | Solutions |
Problem Set 1 [ps] [pdf] [tex] | Feb 5, 2004 | included |
Problem Set 2 [ps] [pdf] [tex] | Feb 10, 2004 | [ps] [pdf] [tex] |
Problem Set 3 [ps] [pdf] [tex] | Feb 12, 2004 | See
Dr. Cox |
Problem Set 4 [ps] [pdf] [tex] | Feb 22, 2004 | [ps] [pdf] [tex] |
Problem Set 5 [ps] [pdf] [tex] | Mar 4, 2004 | [ps] [pdf] [tex] |
Problem Set 6 [ps] [pdf] [tex] | Mar 30, 2004 |
[ps] [pdf] [tex] |
Problem Set 7 [ps] [pdf] [tex] | voluntary |
office hours |
TEST (Rice only) [ps] [pdf] [tex] | last day of finals |
office hours |
Homework is due at the beginning of class on the due date. After the due date, but before solutions are handed out, homework can be turned in for 50% credit. In this case, please slip your homework under the instructors's office door, or bring it to class. After solutions are handed out, 0% credit will be issued. You are encouraged to work in groups for homeworks but you will hand in your own solution which you are expected to understand.
[Outline] [Textbooks] [Grading] [Reading] [Homework problems and solutions]