On the Skorokhod Representation Theorem

الأصل · EN

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 α 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 α. an interesting feature of our result is that we can fix the endpoints ("boundary values") of the lifting of α, as long as their distribution correspond to the endpoints ("boundary values") of α. We also discuss an n-dimensional generalization of this result.