I am looking for book(s) to learn Malliavin Calculus from. Some books that I have come across are,

  1. Stochastic Analysis By Paul Malliavin
  2. Malliavin Calculus for Levy processes with Applications to Finance by Oksendal et al.
  3. The Malliavin calculus and related topics by David Nualart

I was looking for feedback on these books in terms of ease of reading, rigor and coverage of topics. I would also like to know about other books on the topic.

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    $\begingroup$ Simple googling give plethora of issue: $\endgroup$ – Zbigniew Aug 10 at 9:51

Malliavin's stochastic analysis is rather difficult, it's mostly approachable when you've already gotten familiar with the themes of Malliavin Calculus (it assumes familiarity across several topics, in and outside probability). I personally don't like Oksendal's writings because he's a financially focused researcher, but if that's what you're aiming for then go ahead. Also the focus on Lévy processes seems misdirected in the scope of introductory Malliavin calculus. Nualart's book is a standard in the area and a more complete intro than Malliavin's, but it's not an easy read either, but out of your suggestions it is my pick.

Other than that, Kunze's lecture note An Introduction to Malliavin Calculus covers the classical topics among Malliavin's proof of H\"ormander's theorem, as does Hairer's notes Advanced Stochastic Analysis but with more physical intuition. These are free, and I would suggest to skim through one of these before heading for Nualart or Malliavin.


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