I've been reading "Essentials of Stochastic Processes" (second edition) by "Richard Durrett" and I quite liked it, it's a nice size book and it's very easy to read.
However, and this is quite a big one, it doesn't use normal terminology, in fact it re-uses terms in a less sensible way.
For example it defines two states as communicating as $x\rightarrow y$ meaning you can get from x to y. Everything else defines this as "x leading to y" and use communication to mean $x\rightarrow y\text{ and }y\rightarrow x$ (I can't do the double arrow in LaTeX, what's the symbol?).
It also never looks at communicating classes, uses "inessential" "essential", there is only a tiny bit where generating functions are involved - a topic easily worth a chapter.
Should I return this book to the library?
Can you recommend any books?
Recommendation on stochastic process books yes there is something that asks just that, but I looked at these and learnt that having "stochastic processes" in the title does not mean Markov Chains, this could be my fault for not knowing there was a difference (or at least that big of a difference).
One book I have withdrawn from the library is "Introduction to Probability Theory and Stochastic Processes" - a huge book, there's nothing I recogse in it, classification of states isn't there, so can you recommend any books that look at stochastic processes with a focus on Markov Chains?
\Rightarrow(notice the uppercase R) – Ruslan May 18 '14 at 06:04\implies)? What should I have used a capital R for? – Alec Teal May 18 '14 at 06:06(I can't do the double arrow in LaTeX, what's the symbol?). – Ruslan May 18 '14 at 06:58