Markov Processes (graduate course in mathematics)
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Note
Despite the fact that this course is titled Markov Processes, it is, in essence, a light-hearted
version of the subject.
Prerequisites
- Undergraduate probability, including basic elements of stochastic processes
- Some linear algebra and a bit of combinatorics and graph theory
- Recursions and differential equations
- Statistics is NOT required
- You must have studied undergraduate probability from a book where it's done right
Some additional notes and problems
- Stirling's approximation
- Canonical scale
- Optimal stopping
- Options made EZ (pronounce using North American phonology)
- Easy problems
Sample bibliography
- Notes from an undergraduate course in Markov chains and random walks
- P. Bremaud. Markov Chains, Gibbs Fields, Monte Carlo Simulation, and Queues. Springer, 1999 (roughly at the same level as this course)
- J.R. Norris. Markov Chains. Cambridge, 1998 (roughly at the same level as this course)
- E.B. Dynkin and A.A. Yushkevich. Markov processes: theorems and problems. Plenum Press, 1969 (useful for this course)
- E. Cinlar. Introduction to Stochastic Processes. Prentice Hall, 1975 (gives broader perspective)
- D.W. Stroock. An Introduction to Markov Processes. Springer, 2005 (from a graduate course in mathematics at MIT; more advanced than this course)
- G.F. Lawler. Random Walk and the Heat Equation. AMS, 2010 (for general audience; links to analysis)
- B. Toth's notes on Markov chains in finite state space (optional)