This thesis consists of two novel contributions to the computation of first passage time distribution for Brownian motion. First, we extend the known formula for boundary crossing probabilities for Brownian motion to the discontinuous piecewise linear boundary. Second, we derive explicit formula for the first passage time density of Brownian motion crossing piecewise linear boundary. Further, we demonstrate how to approximate the boundary crossing probabilities and density for general nonlinear boundaries. Moreover, we use Monte Carlo simulation method and develop algorithms for the numerical computation. This method allows one to assess the accuracy of the numerical approximation. Our approach can be further extended to compute two-sided boundary crossing probabilities.

The first half of this thesis deals with the line of thought that leads to the development of discrete games of chance as models in statistical physics, with an emphasis on analysis of Parrondo’s games. The second half of the thesis is concerned with applying discrete games of chance to the modelling of other phenomena in the discipline of electrical engineering. The important features being the element of switching that is implicit in discrete games of chance and the element of uncertainty, introduced by the random aspect of discrete games of chance. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1474722 / Thesis (Ph.D.) - University of Adelaide, School of Electrical and Electronic Engineering, 2009

Thesis (Ph. D.)--University of Oregon, 2008. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 122-127). Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Alabama at Birmingham, 2008. / Additional advisors: Renato Camata, Nikolai Chernov, Perry A. Gerkines, Gunter Stolz. Description based on contents viewed Feb. 9, 2009; title from PDF t.p. Includes bibliographical references (p. 123-129).

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 39-40). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 39-40). Also available on the Internet.

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 118-120).

Thesis (Ph. D.)--University of Washington, 1999. / Vita. Includes bibliographical references (leaves 42-43).

Thesis (Ph.D.) - University of Queensland, 2003. / Includes bibliography.