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Extensions of Skorohod’s almost sure representation theorem Open Access


Other title
Convergence in probability
Weak convergence of probability measures
Skorohod’s a. s. representation theorem
Type of item
Degree grantor
University of Alberta
Author or creator
Hernandez Ceron, Nancy
Supervisor and department
Schmuland, Byron (Mathematical and Statistical Sciences)
Examining committee member and department
Beaulieu, Norman C. (Electrical and Computer Engineering)
Litvak, Alexander (Mathematical and Statistical Sciences)
Department of Mathematical and Statistical Sciences

Date accepted
Graduation date
Master of Science
Degree level
A well known result in probability is that convergence almost surely (a.s.) of a sequence of random elements implies weak convergence of their laws. The Ukrainian mathematician Anatoliy Volodymyrovych Skorohod proved the lemma known as Skorohod’s a.s. representation Theorem, a partial converse of this result. In this work we discuss the notion of continuous representations, which allows us to provide generalizations of Skorohod’s Theorem. In Chapter 2, we explore Blackwell and Dubins’s extension [3] and Fernique’s extension [10]. In Chapter 3 we present Cortissoz’s result [5], a variant of Skorokhod’s Theorem. It is shown that given a continuous path inM(S) it can be associated a continuous path with fixed endpoints in the space of S-valued random elements on a nonatomic probability space, endowed with the topology of convergence in probability. In Chapter 4 we modify Blackwell and Dubins representation for particular cases of S, such as certain subsets of R or R^n.
License granted by Nancy Hernandez Ceron ( on 2010-07-07T23:36:21Z (GMT): Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of the above terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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