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Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues (Texts in Applied Mathematics) Hardcover – March 1, 2008
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Top customer reviews
- it's not an intro probability book, make sure you are comfortable with probability to some extent and maybe some random processes. if you want an intro probability book, maybe the Bertsekas would be ok?
- the examples are relevant if a little dated, like not a lot of ppl now probably even remember ALOHA protocol being a thing
- it helps to know some linear algebra and stuff
- it goes over gibbs fields, MCMC, stuff like that in detail and why it works
For a more detailed chapter by chapter account of the book's contents see the review by Carlson.
It explains key ideas, like a transition matrix. Which is usually defined for a discrete time Markov process, but can in fact be generalised to an infinite dimensional state space. From the matrix approach, we get a transition graph and cycles. Then, ergodic behaviour is studied, with invariant measures being found to characterise a given chain.
Bremaud also covers applications of Markov chains. He treats phase transitions and spontaneous magnetisation. Then there are queuing problems and Monte Carlo simulations. The latter can be used in simulated annealing; which in turn can be put to a wide range of problems.