Rice University
This course covers the theory of some of the stochastic processes used
most frequentlyin application:
discrete and continuous time Markov chains, Poisson and renewal processes,
and Brownian motion
Instructor
Dr. Rudolf RiediAssistant
Duncan Hall 2082, 713 / 348 3020,
Jong Soo LeeTime and Place
According to the official Rice web page.
Tuesday Thursday 9:25-10:40 am, Room RH 305 in Rayzor Hall
Monday 5:15 pm (DH 2082), or by appointment
Outline and suggested topics
Textbook
Further suggested reading
- S. Resnick, `Adventures in Stochastic Processes'.
The course will closely follow this book; it is available at the campus bookstore.
Also, Amazon quotes currently (4/2005) a prize reduction by 14%
Grading
20% QUIZ
30% Midterm EXAM
30% Last EXAM
20% Homework
[Outline] [Textbooks] [Grading] [Reading assignment] [Homework problems and solutions] [Tests][Knowledge Milestones]
Classes and Reading assignments
This doubles as a calendar for the course.See also the course schedule from Fall 2003
Covered material | Reading: Resnick (2002) | |
August 23 | Orientation, overview |
|
August 25 |
Review Fubini & convergence, Probability generating function (pgf), moments | 1-8 |
August 30 |
pgf, Simple branching process | 9-17, 18-20 |
September 1 | Extinction, Continuity, Simple random walk |
21-26, 27-29, 33-34 |
September 6 | First Hit at 1, stopping times, Wald's identity | 34-39, 44-45, 47-48 |
September 8 | Markov Chains basics | 60-72 |
September 13 | Chapman-Kolmogorov, Accessible states | 72-79 |
September 15 | Classes, Closed sets, Dissection Principle | 80-84 |
September 20 | Quiz | in class |
September 22 | Class Cancelled due to Hurricane
Rita |
|
September 27 | Transience, Recurrence, Periodicity, Canonical Decomposition | 85-99 |
September 29 | Finite closed classes, Invariant
Distributions |
100-118 |
October 4 | Time averages, limiting distributions |
118-124 |
October 6 | Ergodicity. Make-up quiz |
124-132 |
October 11 | Recess | |
October 13 | Discussing Quiz. Poisson processes: basics, transformation.
Marking |
300-318 |
October 18 | Poisson processes: marking, thinning; Laplace functional | 316-320; 333-336 |
October 20 | Poisson processes: general construction | 337-346 |
October 25 | Order statistics and records; Compound Poisson | 346-349; 330-331 |
Up to here | Material for Test 1 | |
October 27 | Renewal processes: basics, Convolution | 174-176, 176-184 |
November 1 | Renewal function, Renewal equation | 186-187, 197-205 |
November 3 | exponential inter-arrival times, Poisson process | 211,182 |
November 3 | Hand-out 1st Exam | due Nov 11 noon |
November 8 | Limiting theorems | 189-191,212-217,224-227, 237 |
November 10 | Stationary renewal sequences | 214-215,224-229 |
November 15 | Markov processes: def, cond. probabilities | Rao (Probab. Th.), pp 114-135 |
November 17 | Continuous time Markov chains | 367-376 |
November 22 | Forward and Backward Equations | 382-391 |
Up to here | Material for test 2 | |
November 22 | Hand-out 2nd Exam | due last day of class midnight |
November 24 | Thanksgiving | |
November 29 | Review Renewal processes, continuous MC | |
December 1 | Brownian motion, simple properties | 482-484,504-507,494-499 |
December 2 | test 2 due |
[Outline] [Textbooks] [Grading] [Reading assignment] [Homework problems and solutions] [Tests][Knowledge Milestones]
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 8, 2005 | posted Sept 20 [ps] [pdf] [tex] |
Problem Set 2 [ps] [pdf] [tex] | Sept 15, 2005 | posted Sept 20 Problems 5+7: [ps] [pdf] [tex] Problem 6: [pdf] |
Problem Set 3 [ps] [pdf] [tex] | Oct 4, 2005 (grace period due to Rita) | posted Oct 4 [ps] [pdf] [tex] |
Problem Set 4 [ps] [pdf] [tex] | Oct 6, 2005 (grace period due to Rita) | posted Oct 6 [ps] [pdf] [tex] |
Problem Set 5 [ps] [pdf] [tex] | Oct 20, 2005 | posted Oct 26 [ps] [pdf] [tex] |
Problem Set 6 [ps] [pdf] [tex] | Oct 27 | posted Nov 3 [ps] [pdf] [tex] |
Problem Set 7 [ps] [pdf] [tex] | Nov 3 | posted Nov 3 [ps] [pdf] [tex] |
Problem Set 8 [ps] [pdf] [tex] | Nov 22 | posted Nov 22 [ps] [pdf] [tex] |
Problem Set 9 [ps] [pdf] [tex] | Nov 29 | posted Nov 29 [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][Knowledge Milestones]
Quiz (15% towards the grade) | Sept 20 | In class, 60 min, (open: only two hand-written pages ). On preliminaries |
Test 1 (30%) | Due Nov 11 noon. | Take home, 3 hours, On discrete Markov chains and Poisson Point Processes. Open notes: Lecture notes, solutions and all personal notes allowed. |
Test 2 (30%) | Handed out: November 22nd. Due last day of class Dec 2nd. | Take home, 3.5 hours. Open books. On Renewal Processes, and
continuous MC. Download: [ps]
[pdf] |
Knowledge Milestones aquired in this course