On the Skorokhod Representation Theorem

Details On the Skorokhod Representation Theorem On the Skorokhod Representation Theorem

2006-01-22

arxiv.org/abs/math/0601524v1

Mathematics

Probability

Scientific paper

In this paper we present a variant of the well known Skorokhod Representation Theorem. In our main result, given $S$ a Polish space, to a given continous path $\alpha$ in the space of probability measures on $S$, we associate a continuous path in the space of $S$-valued random variables on a nonatomic probability space (endowed with the topology of the convergence in probability). We call this associated path a lifting of $\alpha$. an interesting feature of our result is that we can fix the endpoints ("boundary values") of the lifting of $\alpha$, as long as their distribution correspond to the endpoints ("boundary values") of $\alpha$. We also discuss an $n$-dimensional generalization of this result.

Affiliated with

Also associated with

No associations

Rating

On the Skorokhod Representation Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Skorokhod Representation Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Skorokhod Representation Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-601536