What are some good textbooks to learn probability theory at a graduate level (measure theory and all that)? I have read most of Durrett and it's a pretty good book, but I was hoping for another approach to the subject. If possible, it would be great if the reference focused on random walks and markov chains.
In my personal experience, the following texts proved very useful from a graduate standpoint
- Foundations of Modern Probability, by O. Kallenberg;
- Probability Theory I (Graduate Texts in Mathematics), by M. Loeve;
- Probability Theory, by A. Klenke;
- A Probability Path, by S. Resnick.
These are my top four, but there are naturally other options, depending on your taste and what area of probability theory you're more interested in.
Interesting real-life examples can be found in
- A First Look at Rigorous Probability Theory, by Jeffrey Rosenthal.
Hope this helps!