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)

An important prerequisite for running a successful insurance business is to predict risk. By forecasting the future in as much detail as possible, competitive advantages are created in terms of price differentiation. This work aims at using spatial point processes to provide a proposal for how the geographical position of the customer can be used in developing risk differentiation tools. For spatial variation in claim frequency an approach is presented which is common in spatial epidemiology by considering a group of policyholders, with and without claims, as a realisation of a multivariate Poisson point process in two dimensions. Claim costs are then included by considering the claims as a realisation of a point process with continuous marks. To describe the spatial variation in relative risk, demographic and socio-economic information from Swedish agencies have been used. The insurance data that have been used come from the insurance company If Skadeförsäkring AB, where also the work has been carried out. The result demonstrates problems with parametric modelling of the intensity of policyholders, which makes it difficult to validate the spatial varying intensity of claim frequency. Therefore different proposals of non-parametric estimation are discussed. Further, there are no tendencies that the selected information is able to explain the variation in claim costs. / En viktig förutsättning för att kunna bedriva en framgångsrik försäkringsverksamhet är att prediktera risk. Genom att på en så detaljerad nivå som möjligt kunna förutse framtiden skapas konkurrensfördelar i form av prisdifferentiering. Målet med detta arbete är att med hjälp av spatiala punktprocesser ge ett förslag på hur kunders geografiska position kan utvecklas som riskdifferentieringsverktyg. För spatial variation i skadefrekvens presenteras ett tillvägagångssätt som är vanligt inom spatial epidemiologi genom att betrakta en grupp försäkringstagare, med och utan skador, som en realisering av en multivariat Poissonprocess i två dimensioner. Skadekostnaderna inkluderas sedan genom att betrakta skadorna som en punktprocess med kontinuerliga märken. För att beskriva spatial variation i relativ risk används demografisk och socioekonomisk information från svenska myndigheter. De försäkringsdata som använts kommer från If Skadeförsäkring AB, där också arbetet har utförts. Resultatet påvisar problem med att parametriskt modellera intensiteten för försäkringstagare, vilket medför svårigheter att validera den skattade spatiala variationen i skadefrekvens, varför olika ickeparametriska förslag diskuteras. Vidare upptäcktes inga tendenser till att variationen i skadekostnad kan förklaras med den utvalda informationen.

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.