I'm looking for a reference (books, notes, lectures) which helps a physicist to understand the language of measure theory in the context of stochastic processes (in particular markov chains).

I've studied markov chains and measure theory but now I'm looking for something which helps me filling the gap and making this two topics converge.

I've already read: Measure, Integral and Probability - Marek Capinski, Peter E. Kopp

Maybe something with direct comparison (which writes the same probability both at a basic level and in measure theory) would be great!

Thanks in advance!

  • $\begingroup$ probability with martingales? a lot of people on Math SE seem to like that. there are some mentions of markov chains but I skipped those so I don't know if those parts are good $\endgroup$ – BCLC Dec 15 '15 at 23:31
  • $\begingroup$ Actually what did you find in the last year and a half? $\endgroup$ – BCLC Dec 15 '15 at 23:34
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    $\begingroup$ Well, sadly, nothing to be honest! I simply got used to the new language. $\endgroup$ – edwineveningfall Dec 15 '15 at 23:42
  • $\begingroup$ :)) math.stackexchange.com/questions/11267 $\endgroup$ – BCLC Dec 15 '15 at 23:45
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    $\begingroup$ ahahahah that's true indeed! I was looking at my collection and indeed there is a book "Stochastic Processes for Physicists" by Kurt Jacobs which has a nice chapter 10 on modern probability formulation. $\endgroup$ – edwineveningfall Dec 15 '15 at 23:48

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