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I know this question has been asked several times (see: here, here, here, here, and here), but what are the "best" books on stochastic calculus: has anyone had experience with enough books on this topic so to be able to provide a unified list of books?

More specifically, assuming prior exposition to measure-theoretic probability, what is the best introduction to stochastic calculus, that is the book that keeps your hand the most while not sacrificing math rigour? The books I have in mind for this level, for example, are Kuo, Le Gall, and Oksendal.

Then, what would be the books with intermediate difficulty wrt the unanimous (?) bible Revuz-Yor (possibly listed by increasing difficulty)? The books I have in mind here are Protter and Karatzas-Shreve.

Thank you!

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  • $\begingroup$ I have entirely read the book of Le Gall. It is an excellent introduction to stochastic calculus. If you knew it by heart you would be an excellent MSC student and more than ready for starting a PhD in this field. I have never read Kuo or Okendal so I can't tell. I'm not sure intermediate steps would be necessary before Revuz-Yor. In all cases its reading will be tough. $\endgroup$
    – Will
    Mar 14, 2019 at 10:26
  • $\begingroup$ As intermediate steps I intended books of intermediate difficulty, rather than intermediate readings: I'll update the question to be more clear. Thanks for your comment. $\endgroup$
    – oibaFox
    Mar 14, 2019 at 10:28

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I have found Basic Stochastic Processes by Zdzislaw Brzezniak and Thomasz Zastawniak very good because of all the worked examples. It isn't too expensive (for a maths book at this level) and it has really helped me get through the semester. I have also been using Bernt Oksendal's book that you mention and that is clearly written.

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    $\begingroup$ I cannot cast the vote because I have low reputation points, but thank you for the comment. $\endgroup$
    – oibaFox
    Mar 16, 2019 at 17:25

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