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.

  • $\begingroup$ Handbook of Stochastic Methods, Probability with Martingales, and possibly Random perturbations of dynamical systems. Those come to mind. $\endgroup$ – Ian Nov 25 '19 at 23:59
  • $\begingroup$ My favorite for measure theoretic probability is K L Chung's book. Breiman is a good book too. $\endgroup$ – Kavi Rama Murthy Nov 26 '19 at 0:19
  • $\begingroup$ Adventures in Stochastic Processes by Sidney Resnick has a chapter on Markov chains and one on random walks. $\endgroup$ – Math1000 Nov 26 '19 at 0:40

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!


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