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STAT 3030 Stochastic Processes, Spring 2012

Notices

Note that there is one slack week in the schedule (the last week).

Lecturer

Tommi Sottinen

Scope

5 cr

Prerequisites

Basic knowledge of probability, calculus and linear algebra.

Course Material

We use the book Sheldon M. Ross: Introduction to Probability Models, 10th Edition, 2010.

Contents and Schedule (Peliminary)

The chapters and (page) numbers refer to the above-mentioned Ross's book.

Week 2: Conditional Probability and Conditional Distribution (Part I)
Pages 97-106. (Definitions for the discrete and the continuous case.) Also, for exercises 1.4 and 1.5 it maybe useful to consult the following Wikipedia pages
Week 3: Conditional Probability and Conditional Distribution (Part II)
Pages 106-125. (Calculation of expectations, variances, and probabilities by conditioning.)
Week 4: Markov Chains (Part I)
Pages 191-193. (Markov chains as stochastic matrices.)
Week 5: Markov Chains (Part II)
Pages 194-199 and 204-213. (Markov models, Chapman-Kolmogorov equations and classification of states.)
Week 6: Markov Chains (Part III)
Pages 214-216 and 228-234. (Limiting probabilities, the Ergodic Theorem (Proposition 4.3) and Gambler's ruin.)
Week 7: Markov Chains (Part IV)
Pages 245-249 and 291-297. (Branching processes and exponential distribution.)
Week 8: The Exponential Distribution and the Poisson process
Pages 301-302, 304-306, 308-310 and 312-318.
Week 9: No lectures or exercises!
Week 10: Queueing Theory
Pages 497-511. (Little's law, steady-state probabilities and M/M/1 queues.)

Exercise Problems

  1. exercise
  2. exercise
  3. exercise
  4. exercise
  5. exercise
  6. exercise
  7. exercise (week 10, 9.3.2012!)
  8. exercise

Lectures

Lectures (by Tommi Sottinen):

  • Wed 8-10 Weeks 2-11 Room F652
  • Thu 8-10 Weeks 2-7 Room F652
  • Thu 8-10 Weeks 8-8 Room F651
  • Thu 8-10 Weeks 9-11 Room F652

Exercises (by Bernd Pape)

  • Fri 10-12 Weeks 3-3 Room D102
  • Fri 10-12 Weeks 4-4 Room D115
  • Fri 10-12 Weeks 5-12 Room D102

Exams

  • Fri 23.3.2012 at 12-15
  • Sat 5.5.2012 at 12-15

Grading

Your grade will be given by the formula

    round( max( 0, min(10p-4, 5) ) )

where

    p = a + 0.5(1-a)b

and a is your percentage of points from the exam and b is the percentage of the exercises you have made.

The additional points b are not transferable beyond the first final exams after the course, i.e. then b=0. Also exam-iteration forfeits additional points b.