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 
OrnsteinUhlenbeck,
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 SDEs of solutions to SDEs 
Oksendal 5.1 
March 16 
Existence and Uniqueness of solutions to SDEs 
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, FeynmanKac equation 
Oksendal 8.1 
April 15 
BlackScholes equation, Chemical system (Project) 
Oksendal 12 
[Outline] [Textbooks] [Grading] [Reading] [Homework problems and solutions]
Homework
(texsource 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]