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My mother language book on stochastic processes is pretty much complete(~500 pages) but would like another one in English, to have in my library.

I'm looking for a similar book containing the following:

Discrete and Continuous Markov Chains

Asymptotic Behaviour of Markov Chains (classification of classes, periodic states, absorbing states, Markov Processes)

Queue Theory (Poisson process, chains(M/M/1, M/M/1/K etc)

Renewal Theory

Semi-Markov Chains, Homogenous Markov Systems

(eg don't flag or mark this question, I've already mentioned it's a reference request, both in the title and the tags).

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$1.$ $\textbf{Probability and Random Processes}$ by Grimmet and Stirzaker

and if you also want a book with solved exercises there is a companion book that has solutions to every exercise:

$2.$ $\textbf{One Thousand Exercises in Probability}$

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  • $\begingroup$ Grimmet and Stirzaker looks nice and complete. Thankfully I already got a book with solved exercises by the same author! $\endgroup$ – Rrjrjtlokrthjji Apr 8 '16 at 14:22
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Assmussen, Applied Probability and Queues is a good place to start.

Having Meyn and Tweedie's "Markov Chains and Stochastic Stability" can be useful at times as well for discrete time theory on fairly general state spaces.

Norris' Markov chains and Stroock's Introduction to Markov Processes may also be handy, though they are both somewhat basic.

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  • $\begingroup$ I didn't like Norris' book. Thank you for the recommendations, at a first reading Assmussen looks quite strict. $\endgroup$ – Rrjrjtlokrthjji Apr 8 '16 at 14:27

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