From a course website for Brownian Motion and Stochastic Calculus

Recommended Reading: R-Rated

  • Stochastic Differential Equations: An Introduction with Applications (6th edition) by B. Oksendal
  • Brownian Motion by P. Morters and Y. Peres

Recommended Reading: X-Rated

  • Continuous Martingales and Brownian Motion by D. Revuz and M. Yor
  • Brownian Motion and Stochastic Calculus by I. Karatzas and S. Shreve

I was wondering what R-rated and X-rated mean here? I only know a little that they are normally used for film ratings. But I suspect the reference books are rated according to their rigorousness and/or difficulty?

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    Perhaps soft-core and hard-core à la porn? – bib Feb 10 '13 at 18:52
  • @bib: Which one is soft and which hard? – Tim Feb 10 '13 at 19:04
  • R is milder (soft) than X (hard) – bib Feb 10 '13 at 19:05
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    He gives his e-mail address on that link. Why not try asking him? It is an odd usage of a rating system. Maybe he is just being clever. – JLG Feb 10 '13 at 19:29
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    Sounds like a cheesy joke made my an American in allusion to film ratings, yes. I'd be very surprised if a book on stochastic calculus were actually sexually explicit! – Noldorin Feb 10 '13 at 20:26

To interpret what is meant here, I think you have to consider a synonym of X-rated: hard core.

I would think that an “X-rated” book on stochastic modeling, then, would be “hard core.” In other words: chock full of intense math, and not very friendly toward the casual hobbyist. Another way to say this might be, “not for the faint of heart.” I can imagine someone issuing a warning: “Don't buy this book if you skipped the prerequisite course.” I'd expect such a text to be on the opposite side of the spectrum of where I'd find Math for Dummies, which, to extend the metaphor, would be a G-rated book.


Yes it's a joke on the R (restricted) and X (adult) cinema classifications.

It means the first two books are moderately complicated and the last two are much more intimidating. The term hard-core, also from the adult entertainment industry, is also used.

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