Poisson Point Processes
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Poisson Point Processes
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Author : Roy L. Streit
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-15
Poisson Point Processes written by Roy L. Streit and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-15 with Technology & Engineering categories.
"Poisson Point Processes provides an overview of non-homogeneous and multidimensional Poisson point processes and their numerous applications. Readers will find constructive mathematical tools and applications ranging from emission and transmission computed tomography to multiple target tracking and distributed sensor detection, written from an engineering perspective. A valuable discussion of the basic properties of finite random sets is included. Maximum likelihood estimation techniques are discussed for several parametric forms of the intensity function, including Gaussian sums, together with their Cramer-Rao bounds. These methods are then used to investigate: -Several medical imaging techniques, including positron emission tomography (PET), single photon emission computed tomography (SPECT), and transmission tomography (CT scans) -Various multi-target and multi-sensor tracking applications, -Practical applications in areas like distributed sensing and detection, -Related finite point processes such as marked processes, hard core processes, cluster processes, and doubly stochastic processes, Perfect for researchers, engineers and graduate students working in electrical engineering and computer science, Poisson Point Processes will prove to be an extremely valuable volume for those seeking insight into the nature of these processes and their diverse applications.
Lectures On The Poisson Process
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Author : Günter Last
language : en
Publisher: Cambridge University Press
Release Date : 2017-10-26
Lectures On The Poisson Process written by Günter Last and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-26 with Mathematics categories.
A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
Point Process Calculus In Time And Space
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Author : Pierre Brémaud
language : en
Publisher: Springer Nature
Release Date : 2020-12-05
Point Process Calculus In Time And Space written by Pierre Brémaud and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-05 with Mathematics categories.
This book provides an introduction to the theory and applications of point processes, both in time and in space. Presenting the two components of point process calculus, the martingale calculus and the Palm calculus, it aims to develop the computational skills needed for the study of stochastic models involving point processes, providing enough of the general theory for the reader to reach a technical level sufficient for most applications. Classical and not-so-classical models are examined in detail, including Poisson–Cox, renewal, cluster and branching (Kerstan–Hawkes) point processes.The applications covered in this text (queueing, information theory, stochastic geometry and signal analysis) have been chosen not only for their intrinsic interest but also because they illustrate the theory. Written in a rigorous but not overly abstract style, the book will be accessible to earnest beginners with a basic training in probability but will also interest upper graduate students and experienced researchers.
Poisson Point Processes And Their Application To Markov Processes
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Author : Kiyosi Itô
language : en
Publisher: Springer
Release Date : 2015-12-24
Poisson Point Processes And Their Application To Markov Processes written by Kiyosi Itô and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-24 with Mathematics categories.
An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion processes, by W. Feller, K. Itô, and H. P. McKean, among others. In this book, Itô discussed a case of a general Markov process with state space S and a specified point a ∈ S called a boundary. The problem is to obtain all possible recurrent extensions of a given minimal process (i.e., the process on S \ {a} which is absorbed on reaching the boundary a). The study in this lecture is restricted to a simpler case of the boundary a being a discontinuous entrance point, leaving a more general case of a continuous entrance point to future works. He established a one-to-one correspondence between a recurrent extension and a pair of a positive measure k(db) on S \ {a} (called the jumping-in measure and a non-negative number m
Point Processes
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Author : D.R. Cox
language : en
Publisher: Routledge
Release Date : 2018-12-19
Point Processes written by D.R. Cox and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-19 with Mathematics categories.
There has been much recent research on the theory of point processes, i.e., on random systems consisting of point events occurring in space or time. Applications range from emissions from a radioactive source, occurrences of accidents or machine breakdowns, or of electrical impluses along nerve fibres, to repetitive point events in an individual's medical or social history. Sometimes the point events occur in space rather than time and the application here raneg from statistical physics to geography. The object of this book is to develop the applied mathemathics of point processes at a level which will make the ideas accessible both to the research worker and the postgraduate student in probability and statistics and also to the mathemathically inclined individual in another field interested in using ideas and results. A thorough knowledge of the key notions of elementary probability theory is required to understand the book, but specialised "pure mathematical" coniderations have been avoided.
An Introduction To Stein S Method
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Author : Andrew Barbour
language : en
Publisher: World Scientific
Release Date : 2005-04-14
An Introduction To Stein S Method written by Andrew Barbour and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-14 with Mathematics categories.
A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. Traditional approaches, for example using Fourier analysis, become awkward to carry through in situations in which dependence plays an important part, whereas Stein's method can often still be applied to great effect. In addition, the method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the distribution to be approximated; it can equally well be normal, or Poisson, or that of the whole path of a random process, though the techniques have so far been worked out in much more detail for the classical approximation theorems.This volume of lecture notes provides a detailed introduction to the theory and application of Stein's method, in a form suitable for graduate students who want to acquaint themselves with the method. It includes chapters treating normal, Poisson and compound Poisson approximation, approximation by Poisson processes, and approximation by an arbitrary distribution, written by experts in the different fields. The lectures take the reader from the very basics of Stein's method to the limits of current knowledge.
Stochastic Geometry
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Author : W. Weil
language : en
Publisher: Springer
Release Date : 2006-10-26
Stochastic Geometry written by W. Weil and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-26 with Mathematics categories.
Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures. This book collects lectures presented at the CIME summer school in Martina Franca in September 2004. The main lecturers covered Spatial Statistics, Random Points, Integral Geometry and Random Sets. These are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents a comprehensive and up-to-date description of important aspects of Stochastic Geometry.
Random Point Processes In Time And Space
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Author : Donald L. Snyder
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Random Point Processes In Time And Space written by Donald L. Snyder and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
This book is a revision of Random Point Processes written by D. L. Snyder and published by John Wiley and Sons in 1975. More emphasis is given to point processes on multidimensional spaces, especially to pro cesses in two dimensions. This reflects the tremendous increase that has taken place in the use of point-process models for the description of data from which images of objects of interest are formed in a wide variety of scientific and engineering disciplines. A new chapter, Translated Poisson Processes, has been added, and several of the chapters of the fIrst edition have been modifIed to accommodate this new material. Some parts of the fIrst edition have been deleted to make room. Chapter 7 of the fIrst edition, which was about general marked point-processes, has been eliminated, but much of the material appears elsewhere in the new text. With some re luctance, we concluded it necessary to eliminate the topic of hypothesis testing for point-process models. Much of the material of the fIrst edition was motivated by the use of point-process models in applications at the Biomedical Computer Labo ratory of Washington University, as is evident from the following excerpt from the Preface to the first edition. "It was Jerome R. Cox, Jr. , founder and [1974] director of Washington University's Biomedical Computer Laboratory, who ftrst interested me [D. L. S.
Statistical Inference And Simulation For Spatial Point Processes
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Author : Jesper Moller
language : en
Publisher: CRC Press
Release Date : 2003-09-25
Statistical Inference And Simulation For Spatial Point Processes written by Jesper Moller and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-25 with Mathematics categories.
Spatial point processes play a fundamental role in spatial statistics and today they are an active area of research with many new applications. Although other published works address different aspects of spatial point processes, most of the classical literature deals only with nonparametric methods, and a thorough treatment of the theory and applications of simulation-based inference is difficult to find. Written by researchers at the top of the field, this book collects and unifies recent theoretical advances and examples of applications. The authors examine Markov chain Monte Carlo algorithms and explore one of the most important recent developments in MCMC: perfect simulation procedures.
Non Life Insurance Mathematics
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Author : Thomas Mikosch
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-21
Non Life Insurance Mathematics written by Thomas Mikosch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-21 with Mathematics categories.
"Offers a mathematical introduction to non-life insurance and, at the same time, to a multitude of applied stochastic processes. It gives detailed discussions of the fundamental models for claim sizes, claim arrivals, the total claim amount, and their probabilistic properties....The reader gets to know how the underlying probabilistic structures allow one to determine premiums in a portfolio or in an individual policy." --Zentralblatt für Didaktik der Mathematik