Li, Chung Fai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 43). / Abstracts in English and Chinese. / Acknowledgement --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Construction of the State Spaces --- p.5 / Chapter 2.1 --- The Sierpinski Gasket --- p.5 / Chapter 2.1.1 --- Neighbourhood in the Sierpinski Gasket --- p.7 / Chapter 2.2 --- The Sierpinski Carpet --- p.9 / Chapter 2.2.1 --- Neighbourhood in the Sierpinski Carpet --- p.10 / Chapter 3 --- Preliminary Random Processes on Each Level --- p.12 / Chapter 3.1 --- The Sierpinski Gasket --- p.12 / Chapter 3.1.1 --- Definitions --- p.12 / Chapter 3.1.2 --- Properties of the Random Walk --- p.13 / Chapter 3.1.3 --- Preparations for convergence and continuity --- p.16 / Chapter 3.2 --- The Sierpinski Carpet --- p.19 / Chapter 3.2.1 --- The Brownian Motion Bn on Cn --- p.19 / Chapter 3.2.2 --- Properties of Bm(t) --- p.20 / Chapter 3.2.3 --- Exit time for Bn --- p.27 / Chapter 4 --- The limiting process --- p.29 / Chapter 4.1 --- The Sierpinski Gasket --- p.29 / Chapter 4.1.1 --- Convergence and continuity --- p.29 / Chapter 4.1.2 --- Extension from to G --- p.31 / Chapter 4.1.3 --- Markov property --- p.33 / Chapter 4.2 --- The Sierpinski Carpet --- p.34 / Chapter 4.2.1 --- Continuity --- p.34 / Chapter 4.2.2 --- Existence of Markov process on C --- p.37 / Chapter 4.2.3 --- Piecing Together --- p.38 / Bibliography --- p.43
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326349 |
| Date | January 2008 |
| Contributors | Li, Chung Fai., Sierpinski, Waclaw , 1882-1969, Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, iv, 43 p. : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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