Markov Point Processes And Their Applications
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Markov Point Processes And Their Applications
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Author : M N M van Lieshout
language : en
Publisher: World Scientific
Release Date : 2000-07-12
Markov Point Processes And Their Applications written by M N M van Lieshout and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-12 with Mathematics categories.
These days, an increasing amount of information can be obtained in graphical forms, such as weather maps, soil samples, locations of nests in a breeding colony, microscopical slices, satellite images, radar or medical scans and X-ray techniques. “High level” image analysis is concerned with the global interpretation of images, attempting to reduce it to a compact description of the salient features of the scene. This book takes a stochastic approach. It studies Markov object processes, showing that they form a flexible class of models for a range of problems involving the interpretation of spatial data. Applications can be found in statistical physics (under the name of “Gibbs processes”), environmental mapping of diseases, forestry, identification of ore structure in materials science, signal analysis, object recognition, robot vision, and interpretation of images from medical scans or confocal microscopy. Contents:Point Processes:Definitions and NotationSimple Point ProcessesFinite Point ProcessesMarkov Point Processes:Ripley–Kelly Markov Point ProcessesThe Hammersley–Clifford TheoremMarkov Marked Point ProcessesStatistics Inference:The Metropolis–Hastings AlgorithmConditional SimulationSpatial Birth-and-Death ProcessesApplications:Modelling Spatial PatternsPairwise Interaction ProcessesArea-Interaction Processesand other papers Readership: Undergraduate and postgraduate students; a reference book for researchers in probability & statistics, or engineers interested in spatial data and image analysis. Keywords:Conditional Intensity;Gibbs Process;Interaction Modelling;Markov Point Process;Spatial Statistics;Spatial Inference;Stochastic Geometry;Marked Point Process;Markov Chain Monte CarloReviews:“The book is remarkable by the amount of the material covered and excellent readability … It is highly recommended as the first comprehensive text that covers various concepts related to Markov point processes and typically scattered in the journal literature.”Mathematical Reviews
Markov Point Processes And Their Applications
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Author : M. N. M. Van Lieshout
language : en
Publisher: World Scientific
Release Date : 2000
Markov Point Processes And Their Applications written by M. N. M. Van Lieshout and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This text employs a stochastic approach to studying Markov object processes, showing that they form a flexible class of models for a range of problems involving the interpretation of spatial data. Applications can be found in many fields of study.
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 Process Theory And Applications
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Author : Martin Jacobsen
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-27
Point Process Theory And Applications written by Martin Jacobsen 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 2006-07-27 with Mathematics categories.
Mathematically rigorous exposition of the basic theory of marked point processes and piecewise deterministic stochastic processes Point processes are constructed from scratch with detailed proofs Includes applications with examples and exercises in survival analysis, branching processes, ruin probabilities, sports (soccer), finance and risk management, and queueing theory Accessible to a wider cross-disciplinary audience
An Introduction To Stochastic Processes And Their Applications
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Author : Petar Todorovic
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Introduction To Stochastic Processes And Their Applications written by Petar Todorovic 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 Mathematics categories.
This text on stochastic processes and their applications is based on a set of lectures given during the past several years at the University of California, Santa Barbara (UCSB). It is an introductory graduate course designed for classroom purposes. Its objective is to provide graduate students of statistics with an overview of some basic methods and techniques in the theory of stochastic processes. The only prerequisites are some rudiments of measure and integration theory and an intermediate course in probability theory. There are more than 50 examples and applications and 243 problems and complements which appear at the end of each chapter. The book consists of 10 chapters. Basic concepts and definitions are pro vided in Chapter 1. This chapter also contains a number of motivating ex amples and applications illustrating the practical use of the concepts. The last five sections are devoted to topics such as separability, continuity, and measurability of random processes, which are discussed in some detail. The concept of a simple point process on R+ is introduced in Chapter 2. Using the coupling inequality and Le Cam's lemma, it is shown that if its counting function is stochastically continuous and has independent increments, the point process is Poisson. When the counting function is Markovian, the sequence of arrival times is also a Markov process. Some related topics such as independent thinning and marked point processes are also discussed. In the final section, an application of these results to flood modeling is presented.
Marked Point Processes On The Real Line
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Author : Günter Last
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-08-10
Marked Point Processes On The Real Line written by Günter Last 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 1995-08-10 with Mathematics categories.
This book gives a self-contained introduction to the dynamic martingale approach to marked point processes (MPP). Based on the notion of a compensator, this approach gives a versatile tool for analyzing and describing the stochastic properties of an MPP. In particular, the authors discuss the relationship of an MPP to its compensator and particular classes of MPP are studied in great detail. The theory is applied to study properties of dependent marking and thinning, to prove results on absolute continuity of point process distributions, to establish sufficient conditions for stochastic ordering between point and jump processes, and to solve the filtering problem for certain classes of MPPs.
Point Processes And Their Statistical Inference
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Author : Alan Karr
language : en
Publisher: Routledge
Release Date : 2017-09-06
Point Processes And Their Statistical Inference written by Alan Karr and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-06 with Mathematics categories.
Maintaining the excellent features that made the first edition so popular, this outstanding reference/text presents the only comprehensive treatment of the theory of point processes and statistical inference for point processes-highlighting both pointprocesses on the real line and sp;,.tial point processes. Thoroughly updated and revised to reflect changes since publication of the firstedition, the expanded Second EdiLion now contains a better organized and easierto-understand treatment of stationary point processes ... expanded treatment ofthe multiplicative intensity model ... expanded treatment of survival analysis . ..broadened consideration of applications ... an expanded and extended bibliographywith over 1,000 references ... and more than 3('() end-of-chapter exercises.
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.
Elements Of The Theory Of Markov Processes And Their Applications
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Author : Albert T. Bharucha-Reid
language : en
Publisher: Courier Corporation
Release Date : 1997-01-01
Elements Of The Theory Of Markov Processes And Their Applications written by Albert T. Bharucha-Reid and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.
Graduate-level text and reference in probability, with numerous scientific applications. Nonmeasure-theoretic introduction to theory of Markov processes and to mathematical models based on the theory. Appendixes. Bibliographies. 1960 edition.
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.