The best elementary (and non-trivial) introduction to Markov Chains is Introduction to
Probability (1988), by J L Snell, Random House, NY. It is out of print... however it has
returned as Introduction to Probability, Second Edition (2000) by Grinstead and Snell.
and is available for free at:
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html
In particular, look at Chapter 11 Markov Chains, and then Chapter 12 Random Walks as well:
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.pdf
After this treatment, most text material on Markov Processes will flow better.
Enjoy,
Al
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