Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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!

share|cite|improve this question
"Probability With a View Towards Statistics" in two volumes, by J. Hoffman-Jorgensen. – Michael Greinecker Feb 17 '13 at 20:11
@MichaelGreinecker: Thanks! I remember I heard that book from you or someone else a while ago. But I haven't been able to find an electronic copy. – Tim Feb 17 '13 at 20:19
I've only seen a physical copy of that book. There is also a classic in advanced probability, "Probabilities and potential" by Dellacherie and Meyer, which comes in three volumes. – Michael Greinecker Feb 17 '13 at 20:27
@Tim : I can cite the book of Shiryaev and Jacod "Limit theorems for stochastic Process" which IMO a monument. But with high pre requisit on theory of stochastic processes and probability. – TheBridge Feb 17 '13 at 22:35
@TheBridge: Thanks, that one is great! – Tim Feb 17 '13 at 22:59

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.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.