Download or read book A Martingale Characterization of Mixed Poisson Processes written by Dietmar Pfeifer and published by . This book was released on 1985 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is shown that an elementary pure birth process is a mixed Poisson process if the sequence of post-jump intensities forms a martingale with respect to the delta-fields generated by the jump times of the process. In this case, the post-jump intensities converge a.s. to the mixing random variable of the process. Keyword: Applied probability. (Author).
Download or read book Mixed Poisson Processes written by J Grandell and published by CRC Press. This book was released on 2020-10-28 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 of distributions and processes. The first part of the text gives special emphasis to the estimation of the underlying intensity, thinning, infinite divisibility, and reliability properties. The second part is, to a greater extent, based on Lundberg's thesis.
Download or read book Mixed Poisson Processes written by J Grandell and published by CRC Press. This book was released on 2020-10-29 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 of distributions and processes. The first part of the text gives special emphasis to the estimation of the underlying intensity, thinning, infinite divisibility, and reliability properties. The second part is, to a greater extent, based on Lundberg's thesis.
Download or read book A Martingale Characterization of Quantum Poisson Processes written by Franco Fagnola and published by . This book was released on 1989 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Risk Theory written by and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Twenty-five years ago, Hans Blihlmann published his famous monograph Mathe matical Methods in Risk Theory in the series Grundlehren der Mathematischen Wis8enschaften and thus established nonlife actuarial mathematics as a recognized subject of probability theory and statistics with a glance towards economics. This book was my guide to the subject when I gave my first course on nonlife actuarial mathematics in Summer 1988, but at the same time I tried to incorporate into my lectures parts of the rapidly growing literature in this area which to a large extent was inspired by Blihlmann's book. The present book is entirely devoted to a single topic of risk theory: Its subject is the development in time of a fixed portfolio of risks. The book thus concentrates on the claim number process and its relatives, the claim arrival process, the aggregate claims process, the risk process, and the reserve process. Particular emphasis is laid on characterizations of various classes of claim number processes, which provide alternative criteria for model selection, and on their relation to the trinity of the binomial, Poisson, and negativebinomial distributions. Special attention is also paid to the mixed Poisson process, which is a useful model in many applications, to the problems of thinning, decomposition, and superposition of risk processe8, which are important with regard to reinsurance, and to the role of martingales, which occur in a natural way in canonical situations.
Download or read book A New Characterisation Property of Mixed Poisson Processes Via Berman s Theorem written by Yu Hayakawa and published by . This book was released on 1998 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Processes Theory and Methods written by D N Shanbhag and published by Gulf Professional Publishing. This book was released on 2001 with total page 990 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the series contains chapters on areas such as pareto processes, branching processes, inference in stochastic processes, Poisson approximation, Levy processes, and iterated random maps and some classes of Markov processes. Other chapters cover random walk and fluctuation theory, a semigroup representation and asymptomatic behavior of certain statistics of the Fisher-Wright-Moran coalescent, continuous-time ARMA processes, record sequence and their applications, stochastic networks with product form equilibrium, and stochastic processes in insurance and finance. Other subjects include renewal theory, stochastic processes in reliability, supports of stochastic processes of multiplicity one, Markov chains, diffusion processes, and Ito's stochastic calculus and its applications. c. Book News Inc.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Point Processes and Their Statistical Inference written by Alan Karr and published by Routledge. This book was released on 2017-09-06 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2017. Routledge is an imprint of Taylor & Francis, an Informa company.
Download or read book Abstracts of Communications written by and published by . This book was released on 1998 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non Life Insurance Linked Securities Risk and Pricing Analysis written by Thomas Nowak and published by VVW GmbH. This book was released on 2014-09-25 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unter Insurance-Linked Securities (ILS) versteht man innovative Finanzprodukte, welche Versicherungsrisiken aus den eng abgegrenzten Märkten der Erst- und Rückversicherungswirtschaft herauslösen und mittels Verbriefung auf Kapitalmärkten handelbar machen. Durch ILS erhalten Investoren die Möglichkeit, für die Bereitstellung von Deckungskapital in Versicherungsrisiken zu investieren und im Gegenzug eine Versicherungsprämie zu erhalten. Hierbei verfolgt das Werk zwei Ziele. Zum Einen, die Durchführung einer genauen Analyse der zugrunde liegenden Zahlungsströme, der beworbenen Eigenschaften und jener Risiken, welche mit einer Investition in ILS verbunden sind. Zum Anderen, die Überprüfung der Anwendbarkeit und Passgenauigkeit vorgeschlagener versicherungsmathematischer und marktorientierter Bewertungsverfahren für ILS sowie die Unterbreitung möglicher Vorschläge für Bewertungsverfahren. Da ILS regelmäßig dazu verwendet werden Extremrisiken zu verbriefen, werden beide Untersuchungen unter expliziter Berücksichtigung der statistischen Eigenschaften von Extremrisiken durchgeführt. Im Ergebnis lässt sich festhalten, dass ILS Investitionen mit eigenen Spezifika darstellen. Investoren sollten diese kennen und berücksichtigen. Dies gilt gerade vor dem Hintergrund der stetig steigenden Zahl von ILS, welche insbesondere in den Zeiten der Niedrigzinsphase als attraktives Investment gesehen werden. Das Buch richtet sich an Investoren und Interessierte, die sich über ILS als Investitionen und deren Bewertung informieren möchten.
Download or read book Poisson Processes written by J. F. C. Kingman and published by Clarendon Press. This book was released on 1992-12-17 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 first sight humbler and less worthy of study in its own right. Nearly every book mentions it, but most hurry past to more general point processes or Markov chains. This comparative neglect is ill judged, and stems from a lack of perception of the real importance of the Poisson process. This distortion partly comes about from a restriction to one dimension, while the theory becomes more natural in more general context. This book attempts to redress the balance. It records Kingman's fascination with the beauty and wide applicability of Poisson processes in one or more dimensions. The mathematical theory is powerful, and a few key results often produce surprising consequences.
Download or read book Survival and Event History Analysis written by Odd Aalen and published by Springer Science & Business Media. This book was released on 2008-09-16 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to bridge the gap between standard textbook models and a range of models where the dynamic structure of the data manifests itself fully. The common denominator of such models is stochastic processes. The authors show how counting processes, martingales, and stochastic integrals fit very nicely with censored data. Beginning with standard analyses such as Kaplan-Meier plots and Cox regression, the presentation progresses to the additive hazard model and recurrent event data. Stochastic processes are also used as natural models for individual frailty; they allow sensible interpretations of a number of surprising artifacts seen in population data. The stochastic process framework is naturally connected to causality. The authors show how dynamic path analyses can incorporate many modern causality ideas in a framework that takes the time aspect seriously. To make the material accessible to the reader, a large number of practical examples, mainly from medicine, are developed in detail. Stochastic processes are introduced in an intuitive and non-technical manner. The book is aimed at investigators who use event history methods and want a better understanding of the statistical concepts. It is suitable as a textbook for graduate courses in statistics and biostatistics.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1986 with total page 1362 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on the Poisson Process written by Günter Last and published by Cambridge University Press. This book was released on 2017-10-26 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
Download or read book Statistical Theory and Method Abstracts written by and published by . This book was released on 1999 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Continuous Parameter Markov Processes and Stochastic Differential Equations written by Rabi Bhattacharya and published by Springer Nature. This book was released on 2023-11-16 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate text presents the elegant and profound theory of continuous parameter Markov processes and many of its applications. The authors focus on developing context and intuition before formalizing the theory of each topic, illustrated with examples. After a review of some background material, the reader is introduced to semigroup theory, including the Hille–Yosida Theorem, used to construct continuous parameter Markov processes. Illustrated with examples, it is a cornerstone of Feller’s seminal theory of the most general one-dimensional diffusions studied in a later chapter. This is followed by two chapters with probabilistic constructions of jump Markov processes, and processes with independent increments, or Lévy processes. The greater part of the book is devoted to Itô’s fascinating theory of stochastic differential equations, and to the study of asymptotic properties of diffusions in all dimensions, such as explosion, transience, recurrence, existence of steady states, and the speed of convergence to equilibrium. A broadly applicable functional central limit theorem for ergodic Markov processes is presented with important examples. Intimate connections between diffusions and linear second order elliptic and parabolic partial differential equations are laid out in two chapters, and are used for computational purposes. Among Special Topics chapters, two study anomalous diffusions: one on skew Brownian motion, and the other on an intriguing multi-phase homogenization of solute transport in porous media.
