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Boundary theory of random walk and fractal analysis.January 2011 (has links)
Wong, Ting Kam Leonard. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 91-97) and index. / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Problems of fractal analysis --- p.6 / Chapter 1.2 --- The boundary theory approach --- p.7 / Chapter 1.3 --- Summary of the thesis --- p.9 / Chapter 2 --- Martin boundary --- p.13 / Chapter 2.1 --- Markov chains and discrete potential theory --- p.13 / Chapter 2.2 --- Martin compactification --- p.18 / Chapter 2.3 --- Convergence to boundary and integral representations --- p.20 / Chapter 2.4 --- Dirichlet problem at infinity --- p.25 / Chapter 3 --- Hyperbolic boundary --- p.27 / Chapter 3.1 --- Random walks on infinite graphs --- p.27 / Chapter 3.2 --- Hyperbolic compactification --- p.31 / Chapter 3.3 --- Ancona's theorem --- p.33 / Chapter 3.4 --- Self-similar sets as hyperbolic boundaries --- p.34 / Chapter 3.5 --- Hyperbolic compactification of augmented rooted trees --- p.44 / Chapter 4 --- Simple random walk on Sierpinski graphs --- p.47 / Chapter 4.1 --- Hcuristic argument for d = 1 --- p.48 / Chapter 4.2 --- Symmetries and group invariance --- p.51 / Chapter 4.3 --- Reflection principle --- p.54 / Chapter 4.4 --- Self-similar identity and hitting distribution --- p.60 / Chapter 4.5 --- Remarks and Open Questions --- p.64 / Chapter 5 --- Induced Dirichlet forms on self-similar sets --- p.66 / Chapter 5.1 --- Basics of Dirichlet forms --- p.67 / Chapter 5.2 --- Motivation: the classical Douglas integral --- p.68 / Chapter 5.3 --- Graph energy and the induced forms --- p.69 / Chapter 5.4 --- Induced Dirichlet forms on self-similar sets --- p.74 / Chapter 5.5 --- A uniform tail estimate via coupling --- p.83 / Chapter 5.6 --- Remarks and open questions --- p.89 / Index of selected terms --- p.98
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THE WEAK-CONVERGENCE OF RECURRENT RANDOM-WALK CONDITIONED BY A LATE-RETURN TO ZEROKaigh, William Daniel, 1944- January 1973 (has links)
No description available.
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Uniform convergence sets and random walks via ultraspherical polynomialsNg, Boon-yian. January 1977 (has links)
Thesis--Wisconsin. / Vita. Includes bibliographical references (leaf 81).
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Solving random walk problems using resistive analoguesMorris, Richard D. 01 August 1968 (has links)
The classical method of solving random walk problems involves using Markov chain theory. When the particular random walk of interest is written in matrix form using Markov chain theory, the problem must then be solved using a digital computer. To solve all but the most trivial random walk problems by hand would be extremely difficult and time consuming. Very large random walk problems may even prove difficult to solve on the smaller digital computers. This paper intends to demonstrate a method that may be used to solve large random walk problems in a quick and economical manner. This alternate method uses resistive analogues and has the added feature of extracting particular solutions without having to completely solve the problem as would be necessary using a digital computer. Many analogues of random walks may also be quickly amended to include other random walks with relative ease using this alternate method of solution. Because this method uses nothing more than a power supply, a DC voltmeter and a set of resistors, the analogue of a particular random walk problem may be left set-up without incurring any loss of time or money on a digital computer. Once the resistors are mounted in a permanent fashion, the random walk analogues may also be used as an effective demonstration of random walk probabilities in the classroom.
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Applications of random walksHeard, Perry L. 01 April 2000 (has links)
No description available.
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Random walk in networks : first passage time and speed analysis /Lau, Hon Wai. January 2009 (has links)
Includes bibliographical references (p. 131-134).
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Bounding the edge cover time of random walks on graphsBussian, Eric R. 08 1900 (has links)
No description available.
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Geometric and analytic properties in the behavior of random walks on nilpotent covering graphsIshiwata, Satoshi. January 1900 (has links)
Thesis (Ph. D.)--Tohoku University, 2004. / "June 2004." Includes bibliographical references (p. 69-72).
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Some applications of the method of the characteristic eventMain, Robert Frazee January 1973 (has links)
A method of integrating over difficult sets in Eⁿ by replacing the characteristic function of the set with a discontinuous integral has been used by Markov, Chandrasekhar, Melzak, and others. This thesis employs this method in some problems arising from random walks. A discussion of the difficulties encountered and suggestions for further study are included. / Science, Faculty of / Mathematics, Department of / Graduate
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Fluctuations in the prices of Canadian common stocks and the random walk hypothesisWalden, Thorn January 1965 (has links)
A stock market speculation scheme proposed by Sidney S. Alexander was tested and was found to be more profitable than would be predicted on the assumption that stock prices perform a random walk with a Gaussian distribution and linear trend. The difference between empirical and theoretical gains was found to be statistically significant.
By means of an F-ratio, it was demonstrated that the statistical estimate of the variance of the population of price fluctuations tends to increase as the size of sample is increased. This is consistent with the assumption that the population actually has an infinite variance, but is not consistent with the behavior which would be predicted by any variety of Gaussian random walk.
The sophisticated quantity theory of money was found to be unable to account for any non-random movements in stock market price indices. / Business, Sauder School of / Graduate
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