Results 1 to 1 of 1

Math Help - An infinite dimensional CDF

  1. #1
    Newbie
    Joined
    Jul 2011
    Posts
    15

    An infinite dimensional CDF

    In a nutshell
    Are there CDFs for infinite sequences of random variables with similar properties to the CDFs for finite-dimensional random vectors?


    In more detail
    Every random variable has a corresponding CDF. The same applies to (finite dimensional) random vectors. The CDF of a RV uniquely determines the RV's distribution. Conversely, it is possible to establish a set of criteria irrespective of an underlying RV in such a way that every CDF associated with a given RV satisfies the criteria and conversely to every function F satisfying the criteria there corresponds a RV whose CDF is F.

    Does the same apply in the case of infinite dimensions? Given an infinite sequence of random variables (defined on the same probability space), is there a CDF associated with this sequence that uniquely determines the joint distribution? If so, is it possible to list a set of criteria which every CDF arising from an infinite sequence of RVs satisfies and such that every function F that satisfies these criteria can be associated with an infinite dimensional sequence of RVs whose CDF is F?
    Last edited by Mishmish; April 17th 2012 at 01:45 AM. Reason: Clearer heading + Grammar
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 3rd 2010, 09:08 PM
  2. Replies: 4
    Last Post: June 25th 2010, 08:37 AM
  3. Replies: 2
    Last Post: May 3rd 2010, 01:38 AM
  4. Proof: infinite set minus a fintie set is infinite
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 24th 2009, 11:54 PM
  5. Replies: 5
    Last Post: January 11th 2009, 12:22 AM

Search Tags


/mathhelpforum @mathhelpforum