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Stochastic Processes (Fall 2008)
MATH 4430 3.0AF
MATH 6602 3.0AF
Announcements and documents will be posted here as they
Note that this is an integrated course. In other words, an undergraduate course (MATH 4430) and a graduate course (MATH 6602) meeting at the same time and in the same room. The lecture material is common to both courses. The courses use different texts however, and graduate students will be assigned different readings and assignments.
- Solutions are now posted for Assignment 3, and for the practice problems posted during the strike.
- I am now out of the country, so when lectures resume, they will be given by Prof. van Rensburg instead. We will set the exam together. For example, I will probably set all the questions for the material I lectured on.
- Our course will have
7 classes. This means we
will trim material from the end, and do some of the remaining topics in
less depth. In particular, the rest of the course will focus on continuous time Markov chains. If Brownian motion is covered at all, it will probably be a quick treatment, that you are not responsible for on the exam.
- Prof. van Rensburg has a new webpage for his portion of the course:
van Rensburg 4430/6602 page
- The midterm that was scheduled for Nov 10 is cancelled. Students will have
so much to do in such a short time, and the final exam will be covering all
that material shortly afterwards, so Prof. van Rensburg has opted to use
the time for covering necessary material. This means that the grade weight to
components of the course needs to be adjusted. Grades will be based on the best of two schemes - either a proportional reweighting of all other material, or a scheme that places more weight on the final (so as not to penalize students who were counting on the 2nd midterm to improve on a 1st midterm score). See Prof. van Rensburg's page for details.
- The course will be using on-line student evaluations. Originally the university was going to open the evaluation system on Nov 12, but that has also been postponed till after the strike.
KT refers to Karlin and Taylor, TK to Taylor and Karlin.
As of Wednesday Nov 5 we have looked briefly at examples of continuous time Markov chains (Poisson processes, birth and death processes, queueing models), and will return to them in detail once we build some of the theory. We have derived the Kolmogorov backward equation, and will next turn to the forward equation.
- Basic terminology (TK chapter 1)
- Conditional probability and expectations (TK sections 2.1, 2.4 / KT section 1.1 and 6.7)
- Discrete time Markov chains - transition matrices (TK sections 3.1-3.3 / KT sections 2.1-2.3)
- First step analysis (TK section 3.4 / KT section 3.3)
- Classification of states - reducibility and periodicity (TK section 4.3 / KT section 2.4)
- Limiting behaviour for finite state chains (TK section 4.1 / KT section 3.1)
- Recurrence and transience (TK section 4.4 / KT sections 2.5-2.7, 3.4)
- Reducible chains (TK section 4.5)
- Continuous time Markov chains (TK chapter 6 / KT chapter 4)
- [Brownian motion (TK chapter 8 / KT chapter 7) omit because of the strike]