General state Markov Chains - references

Question

I am looking for a book on Markov Chains on uncountable state spaces. Ideally, the book shall cover the more usual MC theory (discrete space in both discrete and continuous time) and also that of uncountable state spaces.

One of the most comprehensive book I was able to find was John Stachurski, Economic dynamics: theory and computation, but I would like a reference to a math book. I have done some MC in the past, but I I'd like to have a look at both introductory work and more advanced book.

I have looked to the references in the above work, but unfortunately all books look outdated and only partially covering what I need. The references were:

• Meyn and Tweedie - Markov Chains and Stochastic Stability (this which looked like the more interesting, I could not get my hand on at the local library)
• Taylor J C - An introduction to Measure and Probability
• Breiman L - Probability
• Durret R- Probability: theory and examples

Answer 1

You might be interested in having a look at A First Look at Rigorous Probability Theory by Jeffrey S. Rosenthal?

Or perhaps the following additional references?

Markov Chains by D. Revuz

Markov Chains and Stochastic Stability by S. Meyn and R. Tweedie (this links to a PDF file)