Rice University
This course covers the theory of some of the most frequently used stochastic processes in application: discrete and continuous time Markov chains, Poisson and renewal processes, and Brownian motion
Instructor
Dr. Rudolf RiediAssistant
Duncan Hall 2082, 713 / 348 3020,
Office Hours: W 4-6pm (DH 2082), or by appointment
Mike WakinTime and Place
Tuesday Thursday 10:50 - 12:05 am, Room HB 427 in Herman Brown Hall
For current updates check the official Rice page
Outline and suggested topics
Textbook
Further suggested readingS. Resnick, `Adventures in Stochastic Processes'.
The course will closely follow this book; it is available at the campus bookstore. Also, Amazon quotes the prize $69.95
Grading
15% QUIZ
30% Midterm EXAM
30% Last EXAM
15% Homework
10% Notes and participation in class
[Outline] [Textbooks] [Grading] [Reading assignment] [Homework problems and solutions] [Tests]
Classes and Reading assignments
This doubles as a calendar for the course.
Covered material | Reading: Resnick (2002) | |
August 26 | Orientation, history | |
August 28 | Basic review probability, moments | 1-8 |
September 2 | Probability generating function | 9-17 |
September 4 | Simple branching process | 18-26 |
September 9 | Continuity, simple random walk | 27-29, 33-39 |
September 11 | First Hit, stopping times, Wald | 47-48 |
September 16 | Markov Chains basics | 60-72 |
September 18 | Quiz | in class |
September 23 | Chapman-Kolmogorov, Accessible states | 72-79 |
September 25 | Classes, Closed sets, Dissection | 80-84 |
September 30 | Transience, Recurrence, Periodicity | 85-91 |
October 2 | Canonical Decomposition, Examples | 92-101 |
October 7 | Invariant measures and stationary distributions | 116-122 |
October 9 | Time Averages | 122-132 |
October 14 | Recess | |
October 16 | Limiting Distributions, Ergodicity | 122-136 |
October 21 | Poisson processes: basics, transformation | 300-303, 308-312 |
October 23 | Poisson processes: marking, thinning; Laplace functional | 316-320; 333-336 |
Up to here | Material for Test 1 | |
October 28 | Poisson processes: conditioning on the number of points, Records | 337-348 |
October 30 | Renewal processes: basics | 174-176,185 |
November 3 | Hand-out 1st Exam | due Nov 10 noon |
November 4 | Convolution, Renewal function | 176-184,186-187 |
November 6 | Renewal equation, Poisson | 197-205;211,182 |
November 10 | Test 1 due | |
November 11 | Limiting theorems | 189-191,212-217,224-227, 237 |
November 13 | Stationary renewal sequences | 214-215,224-229 |
November 17 | Markov processes: def, examples | Rao (Probab. Th.), pp 114-135 |
November 18 | Continuous time Markov chains | 367-376 |
November 20 | Forward and Backward Equations | 382-391 |
November 25 | Brownian motion, simple properties | 482-484,504-507,494-499 |
Up to here | Material for test 2 | |
November 27 | Thanksgiving | |
November 28 | Hand-out 2nd Exam | due last day of class midnight |
December 2 | Pathwise construction, Brownian Bridge | 489-493, 524-530 |
December 4 | no class (make up Nov 17) | |
December 5 | test 2 due |
[Outline] [Textbooks] [Grading] [Reading assignment] [Homework problems and solutions] [Tests]
Homework
(tex-source and solutions restricted to Rice University)
This
file is needed to latex the source.
Homework sheet | Due date (in class) | Solutions |
Problem Set 1 [ps] [pdf] [tex] | Sept 11, 2003 | [ps] [pdf] [tex] |
Problem Set 2 [ps] [pdf] [tex] | Sept 16, 2003 | Problems 5+7: [ps] [pdf] [tex] Problem 6: [pdf] |
Problem Set 3 [ps] [pdf] [tex] | Oct 16, 2003 | [ps] [pdf] [tex] |
Problem Set 4 [ps] [pdf] [tex] | Oct 23, 2003 | [ps] [pdf] [tex] |
Problem Set 5 [ps] [pdf] [tex] | Nov 18, 2003 | [ps] [pdf] [tex] |
Problem Set 6 [ps] [pdf] [tex] | Nov 25 | [ps] [pdf] [tex] |
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 assignment] [Homework problems and solutions] [Tests]
Quiz (15% towards the grade) | September 18. | In class, 30 min, (open: only two hand-written pages ), preliminaries |
Test 1 (30%) | download: [ps] [pdf] | Take home, 3 hours, (open notes), discrete MC and Poisson |
Test 2 (30%) | Handed out: Late November. To be scheduled | Take home, 4 hours (open books), continuous MC and Brown |