I hope I'm not missing the point here - let me know of any corrections that I need to make here. I too would appreciate anyone's views on these pdfs, their use, etc. as per James' original question.For stocks/ IR:Obviously log-normal ... see Wilmott!!Variance-Gamma - See P Carr web site for refs and papersGARCH - see Duan paper from 1999 (not available electronically as far as I can make out)CIR - interest ratesCEV - ?? still pops up(These two are both cases of a mean-reverting process with power vol. The pdf involves the modified bessel function of the first kind. For some cases, e.g. SRCEV, you can reduce the option pricing formula quite nicely. See Cox 1976, Schorder 1989, google)Quadratic Volatility - not entirely sure what the pdf looks likeBessel processes - there are some papers by Lipton in RISK. I'm still stuggling with these, and in particular as to what form the pdf takes!There was another distribution recently published in Quant Finance. Can't remember the author name - last year. Tsallis distribution. I believe it is okay, but not (yet) brilliant for stocks.Inverse Gamma was used for Asians (??) Correct me if I'm wrong!!I suppose that one gist here is that any process you can dream up has an associated probablity distribution, even if it can't be written down.