MTH734U/MTHM012:
Topics in Probability and Stochastic Processes
This webpage is maintained by the lecturer Dr Roger Sugden and
contains information relevant to the running of the course in 2009/10
- Course information from
undergraduate and
postgraduate directories.
- Prerequisite:
MTH6130
Probability III (or equivalent) is closely related but is NOT a
prerequisite (and there is practically no overlap). However a very good
knowledge of
MTH5118
Probability II is assumed: this will be reviewed and extended
in the first few lectures
- Assessment: 100% by final exam.
The exam will have duration 3 hours and the rubric will state
"You should attempt all questions. Marks awarded are shown next
to the questions."
- Key Objectives: definitive version now available here.
- Lecture (compulsory): Wednesday 10-12noon, Maths 513.
- Tutorial (strongly recommended): Wednesday 12noon-1pm,
Maths 513.
- Office Hours (tbc): Wednesday
13.45-14.45 & Thursday 09.30-10.30, 13.45-14.45, Maths
312.
Work to be marked should be handed in at the Wednesday lecture; marked
scripts
and example solutions will be available in the following Wednesday's
tutorial and additional help is available during Office Hours.
Notes taken in the lectures should provide a basic outline of the material but these will need to be supplemented by reading the relevant sections of
- Howard M. Taylor and Samuel Karlin, An Introduction to Stochastic Modeling, 3rd Edition (Academic Press).
Alternatively, a slightly more advanced treatment can be found in
- William Feller, An Introduction to Probability Theory and its Applications I (Wiley).
Other textbooks that may be useful include:
- Erhan Çinlar Introduction to Stochastic Processes (Prentice-Hall)
- Geoffrey Grimmett and David Stirzaker Probability and Random Processes (Oxford)
- Samuel Karlin and Howard M. Taylor A First Course in Stochastic Processes
- Samuel Karlin and Howard M. Taylor A Second Course in Stochastic Processes
- Sidney I. Resnick Adventures in Stochastic Processes (Birkhäuser).
- Sheldon M. Ross Introduction to Probability Models (Academic).
Course Outline
The following gives a provisional outline of the topics to be covered. It will be updated during the semester with the weekly handouts and problem solutions added.
- Week 1: Introduction and background
A: Continuous-time Markov Chains
- Week 2: Definitions and descriptions
- Weeks 3&4: Backward and forward equations and their solutions
- Weeks 5&6: Absorption, Stationary distributions, ergodic theorem
- Week 7: Consolidation (no lecture or class)
B: Renewal Phenomena
- Week 8: Definitions and concepts
- Week 9: Asymptotic behaviour
- Week 10: Generalizations and variations
- Week 11: No classes on Wednesday but office hours on Thursday as normal: consolidation!
- Week 12: Discrete renewal theory
Previous exam papers from 2003–2009 are available from the library
website (MAS420,MTHM012).
However, note that the content of the course changes from year to year.
In 2006 and 2007 the focus was on Brownian Motion (not covered for
2009/10). A sample paper
corresponding to this year's syllabus can be found here, but no solutions are currently
available.
Please don't hesitate to get in touch with any problems/queries.
Full contact details can be found on my homepage.