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Extensions of Skorohod’s almost sure representation theorem
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- Author / Creator
- Hernandez Ceron, Nancy
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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. -
- Graduation date
- Fall 2010
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- Type of Item
- Thesis
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- Degree
- Master of Science
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- License
- This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.