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On the Skorokhod representation theorem

Author: Jean Cortissoz
Journal: Proc. Amer. Math. Soc. 135 (2007), 3995-4007
MSC (2000): Primary 60B10
Published electronically: September 7, 2007
MathSciNet review: 2341951
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Abstract: In this paper we present a variant of the well-known Skorokhod Representation Theorem. First we prove, given $ S$ a Polish Space, that to a given continuous path $ \alpha$ in the space of probability measures on $ S$, we can 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 of the lifting of $ \alpha$, as long as their distributions correspond to the respective endpoints of $ \alpha$. Finally, we also discuss and prove an $ n$-dimensional generalization of this result.

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Additional Information

Jean Cortissoz
Affiliation: Departamento de Matemáticas, Universidad de Los Andes, Bogotá DC, Colombia

Received by editor(s): March 16, 2006
Received by editor(s) in revised form: July 6, 2006, and September 11, 2006
Published electronically: September 7, 2007
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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