published_or_final_version / abstract / Statistics and Actuarial Science / Master / Master of Philosophy

Large deviation theory has experienced much development and interest in the last two decades. A large deviation principle is the exponential decay of the probability of increasingly rare events and the computation of a rate or entropy function which measures the rate of decay. Within the probability literature there has been much use made of these rates in diverse applications. These large deviation principles have been discovered for independent and identically distributed random variables, as well as random vectors and these have been extended to some cases of weak dependence. In this thesis we prove large deviation principles for finite dimensional distributions of scaling limits of random measures. Functional approaches to large deviation theory using test functions as dual objects to random measures are also developed. These results are applied to some important classes of models, in particular Poisson point processes, Poisson center cluster processes and doubly stochastic point processes. / Graduation date: 1991

We study two different operational scenarios for a regional air ambulance service-company which has bases in Northern California. Two of these bases serve the land areas encompassed roughly in a circular area of radius 100 miles centered in Gilroy and Salinas, respectively; with a large part of their coverage areas reachable from either base. The base in Salinas currently operates one helicopter only from Thursday to Monday, whereas the base in Gilroy operates one helicopter 24/7. The company is considering extending the operation of one helicopter to 24/7 for its Salinas base. In this study we analyze the operational impacts of that extension, and develop a framework that can be applied towards the study of the ambulance assignment problem faced by small operators. / pa/cb Original. 10/06/05. updated 09/09/2011.

by Wing-yi, Tam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 74-77). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Cox and Lewis' Model and Weibull Process Model / Chapter Section 1 --- Nonhomogeneous Poisson Process (NHPP) --- p.5 / Chapter Section 2 --- Cox and Lewis' Model --- p.7 / Chapter Section 3 --- Weibull Process Model --- p.11 / Chapter Section 4 --- Test of NHPP --- p.14 / Chapter Chapter 3 --- Inference for Geometric Process with Inverse Gaussian Distribution / Chapter Section 1 --- Geometric Process (GP) --- p.18 / Chapter Section 2 --- Inverse Gaussian Distribution (IG) --- p.22 / Chapter Section 3 --- Simulation --- p.25 / Chapter Section 4 --- Conclusion --- p.33 / Chapter Chapter 4 --- Comparison Geometric Process Model and NHPP model in Fitting a Point Process / Chapter Section 1 --- Introduction --- p.34 / Chapter Section 2 --- Real Data Examples --- p.39 / Chapter Section 3 --- Conclusion --- p.45 / Tables and Graphs --- p.48 / Appendices --- p.71 / References --- p.74

Zhang Han. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 44-46). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background Study --- p.4 / Chapter 3 --- "The Cost Function under the (s,c2,c1, S) Policy" --- p.8 / Chapter 4 --- "Determination of the Optimal (s,c2,c1,s) Policy" --- p.16 / Chapter 4.1 --- "The Auxiliary Function lγ(s, c2, C1, 5)" --- p.16 / Chapter 4.2 --- Optimizing Parameters of s(γ) and s(γ) --- p.18 / Chapter 4.3 --- Optimizing Parameters c2 (γ) and c1 (γ) --- p.21 / Chapter 5 --- "Algorithm for Computing the Optimal (s, c2, C1, S) Policy" --- p.27 / Chapter 5.1 --- Brief Description of the Algorithm --- p.27 / Chapter 5.2 --- The Statement of the Algorithm --- p.28 / Chapter 5.3 --- Interpretation of the Algorithm --- p.29 / Chapter 6 --- "The Optimality of the (s, c2，c1, S) Policy" --- p.31 / Chapter 6.1 --- Average Cost Criterion --- p.31 / Chapter 6.2 --- The Proof of Optimality --- p.34 / Chapter 6.3 --- "Optimality Proof for the Modified (s,c2,C1,S) Policy in the Re- laxed Model" --- p.38 / Chapter 6.3.1 --- Introduction of the Relaxed Model --- p.38 / Chapter 6.3.2 --- Average Cost Criteria for the Relaxed Model --- p.38 / Chapter 7 --- Conclusion --- p.42 / Bibliography --- p.43

Thesis (M.S.)--Rochester Institute of Technology, 2009. / Typescript. Includes bibliographical references (leaves 108-110).

Thesis (Ph. D.)--School of Industrial and Systems Engineering, Georgia Institute of Technology, 2004. Directed by Robert D. Foley. / Vita. Includes bibliographical references (leaves 85-86).

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

Thesis (Ph.D.)--University of Melbourne, Dept. of Mathematics and Statistics, 2001. / Typescript (photocopy). Includes bibliographical references (leaves 126-128).

Thesis--Auburn University, 2008. / Abstract. Vita. Includes bibliographic references (p.35).