Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: Non standard probability theory
Replies: 12   Last Post: Dec 19, 2013 8:03 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
danielgoldman@sunyorange.edu

Posts: 5
Registered: 11/9/12
Re: Non standard probability theory
Posted: Nov 11, 2012 9:36 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.