On Sunday, November 11, 2012 4:18:15 PM UTC-5, Ray Vickson wrote: > On Sunday, November 11, 2012 7:38:09 AM UTC-8, kir wrote: > > > What kind of work is being done in probability theory beyond the standard normally used? I know that negative probabilities have been discussed. Is there anything else? > > > > I'm not sure this is what you want, but there has been work in Probability theory using "non-standard analysis", so one can talk about actual infinitesimals, etc. Perhaps the most accessible introduction to this is the old but still good little book by Edward Nelson ("Radically Elementary Probability", Princeton U. Press). You can download a free pdf version from Edward Nelson's home page: just go to his publications list and click on the book title. > > > > RGV
Primarily dealing with nonstandard analysis. I suppose I really need to study measure theory before I can dive in too deep. Dealing with infinitesimals is a great extension in my opinion. It always bothered me that we often define something with probability zero to mean it can't occur, yet even though in the case of an infinite probability distribution X P(X=x) = 0 for all x values. One x value DOES occur.
What's really true is that it occurs with infinitesimal probability.