On the Skorokhod Representation Theorem

Jean Cortissoz

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On the Skorokhod Representation Theorem

Jean Cortissoz

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Abstract

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.

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BibTeX RIS

Jean Cortissoz. 2006-01-22. On the Skorokhod Representation Theorem. https://arxiv.org/abs/math/0601524

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