Applied Stochastic Processes

 STAT 552, Fall 2003

 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

[Outline] [Textbooks] [Grading] [Reading assignment] [Homework problems and solutions] [Tests]


Dr. Rudolf Riedi
Duncan Hall 2082, 713 / 348 3020,
Office Hours: W 4-6pm (DH 2082), or by appointment
Mike Wakin
Time 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


  • S. 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
    Further suggested reading


    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]

    (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]


    Late Homework Policy

    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

    Any student with a documented disability needing academic adjustments or accommodations is requested to speak with me during the first two weeks of class. All discussions will remain confidential. Students with disabilities should also contact Disabled Student Services in the Ley Student Center.
    Aug 1, 2003.  Dr. Rudolf Riedi