Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the ...
In the theory of random processes there are two that are fundamental, and occur over and over again, often in surprising ways. There is a real sense in which the deepest results are concerned with their interplay. One, the Bachelier Wiener model of Brownian motion, has been the subject of many books. The other, the Poisson process, seems at ...
This book discusses the estimation theory for the wide class of inhomogeneous Poisson processes. The consistency, limit distributions and the convergence of moments of parameter estimators are established in regular and non-regular (change-point type) problems. The maximum likelihood, Bayesian, and the minimum distance estimators are investigated ...
This volume is a collection of articles by speakers at the conference "Poisson 2006: Poisson Geometry in Mathematics and Physics", which was held June 5-9, 2006, in Tokyo, Japan. Poisson 2006 was the fifth in a series of international conferences on Poisson geometry that are held once every two years. The aim of these conferences is to bring ...
To date, Mixed Poisson processes have been studied by scientists primarily interested in either insurance mathematics or point processes. Work in one area has often been carried out without knowledge of the other area. Mixed Poisson Processes is the first book to combine and concentrate on these two themes, and to distinguish between the notions ...
A presentation of the state-of-the-art in the field of compound Cox processes and their applications in insurance and finance. Besides a review of well-known classical results on compound and mixed Poisson processes and risk theory, it contains many more recently obtained results by the authors.
This work represents a comprehensive account of all existing methods of statistical estimation for Boolean models. It summarizes the available theory concerning Boolean models in a form accessible for mathematically aware scientists working in stochastic geometry, image analysis and microscopy. Written in lecture note style, it has two levels of ...
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