On the Skorokhod representation theorem
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- by Jean Cortissoz PDF
- Proc. Amer. Math. Soc. 135 (2007), 3995-4007 Request permission
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.References
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Additional Information
- Jean Cortissoz
- Affiliation: Departamento de Matemáticas, Universidad de Los Andes, Bogotá DC, Colombia
- Email: jean.cortissoz@gmail.com
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 3995-4007
- MSC (2000): Primary 60B10
- DOI: https://doi.org/10.1090/S0002-9939-07-08922-8
- MathSciNet review: 2341951