Thesis--Wisconsin. / Vita. Includes bibliographical references (leaf 81).

We present and prove some important theorems regarding determinantal point processes. In particular we focus on existance and uniqueness theorems. Furthermore, we present an algorithm for generating determinantal point processes with a finite-dimensional projection kernel. Also, we go through the mathematical preliminaries required to understand the theory.

Product densities have been widely used in the literature to give a concrete description of the distribution of a point process. A rigorous description of properties of product densities is presented with examples to show that in some sense these results are the best possible. Product densities are then used to discuss positive dependence properties of point processes. There are many ways of describing positive dependence. Two well known notions for Bernoulli random variables are the strong FKG inequalities and association, the strong FKG inequalities being much stronger. It is known, for example, from van den Berg and Burton, that the strong FKG inequalities are equivalent to all conditional distributions being associated, which is equivalent to all conditional distributions being positively correlated. In the case of point processes for which product densities exist, analogs of such positive dependence properties are given. Examples are presented to show that unlike the Bernoulli case none of these conditions are equivalent, although some are shown to be implied by others. / Graduation date: 1988

No description available.

In this dissertation, we consider two aspects of the theory of weak convergence of cadlag processes. / We first give a necessary and sufficient condition for the tightness of a sequence of cadlag processes (chapters 2,3) which generalizes Rebolledo's condition (see 13 ). It is a stochastic condition in the sense that stopping times rather than deterministic times are used in the statement. / We then discuss the predictability of the limit of a sequence of predictable processes (chapters 4-6). For a convergent sequence of point processes we show that, if the sequence of compensators converges, then the limit of compensators is the compensator of the limit of point processes (chapters 4,5). / Finally, we prove in Chapter 6 that extended weak convergence of a sequence of increasing predictable processes ensures the predictability of the limit.

Thesis (Ph. D.)--Oregon State University, 1988. / Typescript (photocopy). Includes bibliographical references (leaves 71-74). Also available on the World Wide Web.

Thesis (Ph. D.)--University of Missouri-Columbia, 2005. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (November 14, 2006) Vita. Includes bibliographical references.

<p> This thesis is concerned with investigating point processes and the numerous methods available for obtaining information about them. </p> / Thesis / Master of Science (MSc)

We consider a data set comprising encounters between gray seals off Sable Island in the autumn of 2009. We apply Spatial Point Pattern data analysis approaches to this data set and demonstrate the effectiveness of these techniques. Specifically we propose using point processes for clustered data; the Inhomogeneous Poisson process, and the subset of cluster processes called Cox processes. We utilize maximum likelihood methods to produce a model for the mean intensity of the seal encounters which includes spatial covariates. We then consider the impact of inhomogeneity and review minimum contrast methods for fitting the Cox process models, specifically the Thomas and Matern cluster processes. We demonstrate that these methods allow us to gain valuable insight into the nature and extent of grey seal encounters at sea. Finally we validate both our conclusions and the approach taken using the most recent data available, that of autumn 2010.

Abstract Not Provided. / Thesis / Master of Science (MSc)