TITLE: Books at similar levels as Kallenberg' Foundation of Modern Probability?
QUESTION [6 upvotes]: Thanks to many people who have mentioned it to me and others on this site before. I was just able to peek into Kallenberg' Foundation of Modern Probability. It is more comprehensive, deep and thorough than the books I have seen before. It not only covers probability theory, but also stochastic processes and calculus, random measures, point processes and other topics. I don't expect myself to understand it fully and easily at all, but I admit it is the best reference I have seen.
I was wondering if you could mention other books at similar (partially) topics and/or levels as Kallenberg' book?
Thanks and regards!

REPLY [5 votes]: One very useful reference is Rogers & Williams: "Diffusions, Markov processes and Martingales". It's not quite as varied in its topics as Kallenberg's book, but it does cover many topics in the theory of stochastic processes - both discrete-time and continuous-time martingales, weak convergence on Polish spaces, regular conditional probabilities, Markov processes and stochastic integration.
The book "Semimartingale theory and stochastic calculus" by He, Wang & Yan is also rather useful when it comes to continuous-time stochastic processes. It covers both parts of the classical "general theory of processes" as is also found in Meyer & Dellacherie, as well as a very good deal of martingale theory, stochastic integration with respect to general semimartingales, and also Girsanov's theorem, martingale representation, various inequalities, random measures and weak convergence of semimartingales.