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Author: Kiyosi Itô Publisher: Springer ISBN: 981100272X Category : Mathematics Languages : en Pages : 43
Book Description
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
Author: Kiyosi Itô Publisher: Springer ISBN: 981100272X Category : Mathematics Languages : en Pages : 43
Book Description
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
Author: Martin Jacobsen Publisher: Springer Science & Business Media ISBN: 0817644636 Category : Mathematics Languages : en Pages : 325
Book Description
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
Author: M N M van Lieshout Publisher: World Scientific ISBN: 1783262508 Category : Mathematics Languages : en Pages : 184
Book Description
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
Author: M. N. M. Van Lieshout Publisher: World Scientific ISBN: 1860940714 Category : Mathematics Languages : en Pages : 185
Book Description
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.
Author: D.R. Cox Publisher: Routledge ISBN: 1351423851 Category : Mathematics Languages : en Pages : 171
Book Description
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.
Author: Roy L. Streit Publisher: Springer Science & Business Media ISBN: 1441969233 Category : Technology & Engineering Languages : en Pages : 274
Book Description
"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.
Author: Alan Karr Publisher: Routledge ISBN: 1351423835 Category : Mathematics Languages : en Pages : 509
Book Description
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.
Author: Günter Last Publisher: Cambridge University Press ISBN: 1107088011 Category : Mathematics Languages : en Pages : 315
Book Description
A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
Author: Petar Todorovic Publisher: Springer Science & Business Media ISBN: 1461397421 Category : Mathematics Languages : en Pages : 302
Book Description
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.
Author: Kiyosi Itô
Author: Kiyosi Itô
Author: Martin Jacobsen
Author: M N M van Lieshout
Author: M. N. M. Van Lieshout
Author: D.R. Cox
Author: Donald Lee Snyder
Author: Roy L. Streit
Author: Alan Karr
Author: Günter Last
Author: Petar Todorovic