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  • http://hdl.handle.net/10048/1205
  • Extensions of Skorohod’s almost sure representation theorem
  • Hernandez Ceron, Nancy
  • en
  • Skorohod’s a. s. representation theorem
    Weak convergence of probability measures
    Convergence in probability
  • Jul 8, 2010 5:06 PM
  • Thesis
  • en
  • Adobe PDF
  • 810314 bytes
  • 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.
  • Master's
  • Master of Science
  • Department of Mathematical and Statistical Sciences
  • Fall 2010
  • Schmuland, Byron (Mathematical and Statistical Sciences)
  • Litvak, Alexander (Mathematical and Statistical Sciences)
    Beaulieu, Norman C. (Electrical and Computer Engineering)

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