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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Extensions of Skorohods almost sure representation theorem

Hernandez Ceron, Nancy 11 1900 (has links)
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 Skorohods 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 Skorohods Theorem. In Chapter 2, we explore Blackwell and Dubinss extension [3] and Ferniques extension [10]. In Chapter 3 we present Cortissozs result [5], a variant of Skorokhods 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. / Mathematics

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