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
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:AEU.10048/1205 |
| Date | 11 1900 |
| Creators | Hernandez Ceron, Nancy |
| Contributors | Schmuland, Byron (Mathematical and Statistical Sciences), Litvak, Alexander (Mathematical and Statistical Sciences), Beaulieu, Norman C. (Electrical and Computer Engineering) |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 810314 bytes, application/pdf |
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