Poisson Processes
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Poisson Processes
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Author : J. F. C. Kingman
language : en
Publisher: Clarendon Press
Release Date : 1992-12-17
Poisson Processes written by J. F. C. Kingman and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-12-17 with Mathematics categories.
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.
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.
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.
Doubly Stochastic Poisson Processes
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Author : J. Grandell
language : en
Publisher: Springer
Release Date : 2006-11-14
Doubly Stochastic Poisson Processes written by J. Grandell and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Basics Of Applied Stochastic Processes
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Author : Richard Serfozo
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-01-24
Basics Of Applied Stochastic Processes written by Richard Serfozo 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 2009-01-24 with Mathematics categories.
Stochastic processes are mathematical models of random phenomena that evolve according to prescribed dynamics. Processes commonly used in applications are Markov chains in discrete and continuous time, renewal and regenerative processes, Poisson processes, and Brownian motion. This volume gives an in-depth description of the structure and basic properties of these stochastic processes. A main focus is on equilibrium distributions, strong laws of large numbers, and ordinary and functional central limit theorems for cost and performance parameters. Although these results differ for various processes, they have a common trait of being limit theorems for processes with regenerative increments. Extensive examples and exercises show how to formulate stochastic models of systems as functions of a system’s data and dynamics, and how to represent and analyze cost and performance measures. Topics include stochastic networks, spatial and space-time Poisson processes, queueing, reversible processes, simulation, Brownian approximations, and varied Markovian models. The technical level of the volume is between that of introductory texts that focus on highlights of applied stochastic processes, and advanced texts that focus on theoretical aspects of processes.
Fundamentals Of Applied Probability And Random Processes
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Author : Oliver Ibe
language : en
Publisher: Elsevier
Release Date : 2005-10-19
Fundamentals Of Applied Probability And Random Processes written by Oliver Ibe and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-19 with Mathematics categories.
This book is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability to real-world problems, and introduce the basics of statistics. The book's clear writing style and homework problems make it ideal for the classroom or for self-study. * Good and solid introduction to probability theory and stochastic processes * Logically organized; writing is presented in a clear manner * Choice of topics is comprehensive within the area of probability * Ample homework problems are organized into chapter sections
A First Course In Stochastic Models
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Author : Henk C. Tijms
language : en
Publisher: John Wiley & Sons
Release Date : 2003-04-18
A First Course In Stochastic Models written by Henk C. Tijms and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-18 with Mathematics categories.
The field of applied probability has changed profoundly in the past twenty years. The development of computational methods has greatly contributed to a better understanding of the theory. A First Course in Stochastic Models provides a self-contained introduction to the theory and applications of stochastic models. Emphasis is placed on establishing the theoretical foundations of the subject, thereby providing a framework in which the applications can be understood. Without this solid basis in theory no applications can be solved. Provides an introduction to the use of stochastic models through an integrated presentation of theory, algorithms and applications. Incorporates recent developments in computational probability. Includes a wide range of examples that illustrate the models and make the methods of solution clear. Features an abundance of motivating exercises that help the student learn how to apply the theory. Accessible to anyone with a basic knowledge of probability. A First Course in Stochastic Models is suitable for senior undergraduate and graduate students from computer science, engineering, statistics, operations resear ch, and any other discipline where stochastic modelling takes place. It stands out amongst other textbooks on the subject because of its integrated presentation of theory, algorithms and applications.
Mixed Poisson Processes
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Author : J Grandell
language : en
Publisher: CRC Press
Release Date : 2020-10-29
Mixed Poisson Processes written by J Grandell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-29 with Mathematics categories.
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.
Discrete Stochastic Processes
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Author : Robert G. Gallager
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Discrete Stochastic Processes written by Robert G. Gallager 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.
Stochastic processes are found in probabilistic systems that evolve with time. Discrete stochastic processes change by only integer time steps (for some time scale), or are characterized by discrete occurrences at arbitrary times. Discrete Stochastic Processes helps the reader develop the understanding and intuition necessary to apply stochastic process theory in engineering, science and operations research. The book approaches the subject via many simple examples which build insight into the structure of stochastic processes and the general effect of these phenomena in real systems. The book presents mathematical ideas without recourse to measure theory, using only minimal mathematical analysis. In the proofs and explanations, clarity is favored over formal rigor, and simplicity over generality. Numerous examples are given to show how results fail to hold when all the conditions are not satisfied. Audience: An excellent textbook for a graduate level course in engineering and operations research. Also an invaluable reference for all those requiring a deeper understanding of the subject.
The Theory Of Stochastic Processes
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Author : D.R. Cox
language : en
Publisher: CRC Press
Release Date : 1977-02-01
The Theory Of Stochastic Processes written by D.R. Cox and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-02-01 with Mathematics categories.
The random walk; Markov chains; Markov processes with discrete states in continuous time; Markov processes in continuous time with continuous state space; Non-markovian processes; Stationary processes: time domain; Stationary processes: frequency domain; Point processes; Appendices; Index.