STAT 846.3 (04)
Stochastic Processes
This course will examine the theory and applications of commonly encountered
stochastic processes, at a level suitable for beginning graduate students.
Students are expected to have a command of elementary probability (both discrete
and continuous), a solid foundation in calculus, and some knowledge of
matrix algebra.
Essential Information
| Instructor:
| Lectures:
| Evaluation:
|
M. Bickis
234 McLean Hall
966-6088
|
TTh 8:30-9:50
MCLN 242.2
|
60% for three problem assignments
40% for the final exam.
|
Recommended text
There is no required text book for the course. Course material will be
presented in the lectures and handouts will be given for assigned problems.
The following books cover most of the material at about the same level of
rigour as this course. The course will most closely follow the sequence of Ross.
- A. K. Basu, Introduction to Stochastic Processes, Alpha Science, 2003.
- Rick Durrett, Essentials of Stochastic Processes, Springer, 1999.
- Edward Kao, An Introduction to Stochastic Processes, Duxbury, 1997.
- Samuel Karlin and Howard Taylor, A First Course in Stochastic Processes, Academic Press, 1975.
- Sheldon Ross, Stochastic Processes, 2nd edition, Wiley, 1996.
(The first
edition is also useful.)
In addition to these references, William Feller's classic An Introduction to Probability Theory and its Applications (2 volumes) is a useful resource for many ideas and interesting examples.
Schedule of Topics
| 1. | Concepts of stochastic processes:
Joint, conditional, and transition probabilities
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| 2. | The Poisson process and generalizations
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| 3. | Renewal processes
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| 4. | Discrete time Markov chains
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| 5. | Continuous time Markov chains
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| 6. | Random walk and Brownian motion.
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