Math 592A: Discrete State Markov Processes and Interacting Particle Systems
Bruce Erickson
Winter 2001, Monday/Wednesday/Friday 1:30-2:20 (tentative time)
Markov processes on countable state spaces are important theoretically
and for their applications. For the first weeks we will go through the
basic theory of these processes. Some of the topics likely to be discussed:
transistion semigroups, generators, hitting times, explosions, boundaries,
exit/entrance decompositions, invariant measures. Not everything will be
proved in detail. Later we will look into parts of one of the important
applications, namely, the vast theory of interacting particle systems.
Recommended texts (which I will put on reserve):
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For discrete space Markov processes: Various chapters in Diffusions,
Markov Processes, and Martingales by D. Williams and L.C.G. Rogers.
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For interacting particle systems: Stochastic interacting systems: contact,
voter, and exclusion processes, by T. Ligget, and/or his earlier book,
Interacting
Particle Systems.