Thesis (Ph. D.)--University of Chicago, Dept. of Economics, June 2000. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (M.S.)--Pennsylvania State University, 2008. / Mode of access: World Wide Web.

In this thesis, we study some geometrical aspects of metric measure spaces (Rn, psi1/2 , mu)where mu is a locally finite regular Borel measure and a metric on psi1/2 which arises from a continuous negative definite function psi : Rn &rarr; R which satisfies psi(xi) &ge; 0 with psi(xi) = 0. This study is motivated by the investigation of a transition density estimate for pure jump processes on a general metric measure space. To gain a better insight into the behaviour of transition functions of symmetric Levy processes in this general setting, it seems desirable to understand geometrical properties of their underlying state spaces. More precisely, we show completeness of the metric spaces (Rn, psi1/2) and study under which circumstances open balls Bpsi(x,r), x &isin; Rn, r > 0, with respect to this metric are convex. Moreover, we focus on conditions of the metric measure spaces (Rn,psi1/2 ,mu) for the balls to satisfy the volume growth property [equation] for mu-almost all x &isin; Rn, 0 < r < R and a constant Cpsi(x,R)&ge;1. Finally, we show that the homogeneity property of a metric measure space can be applied to our case and provide some results associated with the construction of a Hajlasz-Sobolc space over (Rn,psi1/2, lambda(n)),where lambda(n) denotes the n-dirnensional Lebesgue measure.

S.S. Sastry, C. Desoer and P. Varaiya. / Bibliography: leaf 4. / Caption title. "August, 1981." / Supported by DOE under Grant ET-A01-2295T050 NSF Grant ENG-78-09032-A01

S.S. Sastry, C. Desoer and P. Varaiya. / Bibliography: leaf 4. / Caption title. "August, 1981." / Supported by DOE under Grant ET-A01-2295T050 NSF Grant ENG-78-09032-A01

Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of compound Poisson processes whose jumps belong to a finite set A in R^d. We propose a characterization of the reciprocal class as the unique set of probability measures on which a family of time and space transformations induces the same density, expressed in terms of the reciprocal invariants. The geometry of A plays a crucial role in the design of the transformations, and we use tools from discrete geometry to obtain an optimal characterization. We deduce explicit conditions for two Markov jump processes to belong to the same class. Finally, we provide a natural interpretation of the invariants as short-time asymptotics for the probability that the reference process makes a cycle around its current state.

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 102-107).

No description available.

Wu, Tao. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 56-61). / Abstracts in English and Chinese. / Chapter 1 --- Background and Organization --- p.7 / Chapter 2 --- Parallel Talbot method for solving partial integro- differential equations --- p.9 / Chapter 2.1 --- Introduction --- p.9 / Chapter 2.2 --- Initial-boundary value problem --- p.11 / Chapter 2.3 --- Spatial discretization and semidiscrete problem --- p.12 / Chapter 2.4 --- Parallel Talbot method --- p.15 / Chapter 2.4.1 --- Φ-functions and Talbot quadrature --- p.15 / Chapter 2.4.2 --- Control on nonnormality and feasibility con- straints --- p.18 / Chapter 2.4.3 --- Optimal parameterization of parabolic Talbot contour --- p.22 / Chapter 2.5 --- Numerical experiments --- p.26 / Chapter 2.6 --- Conclusion --- p.32 / Chapter 3 --- Memory-reduction Monte Carlo method for pricing American options --- p.37 / Chapter 3.1 --- Introduction --- p.37 / Chapter 3.2 --- Exponential Levy processes and the full-storage method --- p.39 / Chapter 3.3 --- Random number generators --- p.41 / Chapter 3.4 --- The memory-reduction method --- p.43 / Chapter 3.5 --- Numerical examples --- p.45 / Chapter 3.5.1 --- Black-Scholes model --- p.46 / Chapter 3.5.2 --- Merton's jump-diffusion model --- p.48 / Chapter 3.5.3 --- Variance gamma model --- p.50 / Chapter 3.5.4 --- Remarks on the efficiency of the memory-reduction method --- p.52 / Chapter 3.6 --- Conclusion --- p.53 / Chapter 3.7 --- Appendix --- p.54