Introduction To The Statistics Of Poisson Processes And Applications

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Introduction to the Statistics of Poisson Processes and Applications

Yury A. Kutoyants

Author : Yury A. Kutoyants
Publisher : Springer Nature
Page : 683 pages
File Size : 50,6 Mb
Release : 2023-09-04
Category : Mathematics
ISBN : 9783031370540

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Introduction to the Statistics of Poisson Processes and Applications by Yury A. Kutoyants Pdf

This book covers an extensive class of models involving inhomogeneous Poisson processes and deals with their identification, i.e. the solution of certain estimation or hypothesis testing problems based on the given dataset. These processes are mathematically easy-to-handle and appear in numerous disciplines, including astronomy, biology, ecology, geology, seismology, medicine, physics, statistical mechanics, economics, image processing, forestry, telecommunications, insurance and finance, reliability, queuing theory, wireless networks, and localisation of sources. Beginning with the definitions and properties of some fundamental notions (stochastic integral, likelihood ratio, limit theorems, etc.), the book goes on to analyse a wide class of estimators for regular and singular statistical models. Special attention is paid to problems of change-point type, and in particular cusp-type change-point models, then the focus turns to the asymptotically efficient nonparametric estimation of the mean function, the intensity function, and of some functionals. Traditional hypothesis testing, including some goodness-of-fit tests, is also discussed. The theory is then applied to three classes of problems: misspecification in regularity (MiR),corresponding to situations where the chosen change-point model and that of the real data have different regularity; optical communication with phase and frequency modulation of periodic intensity functions; and localization of a radioactive (Poisson) source on the plane using K detectors. Each chapter concludes with a series of problems, and state-of-the-art references are provided, making the book invaluable to researchers and students working in areas which actively use inhomogeneous Poisson processes.

Statistical Inference for Spatial Poisson Processes

Yu A. Kutoyants

Author : Yu A. Kutoyants
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217060

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Statistical Inference for Spatial Poisson Processes by Yu A. Kutoyants Pdf

This work is devoted to several problems of parametric (mainly) and nonparametric estimation through the observation of Poisson processes defined on general spaces. Poisson processes are quite popular in applied research and therefore they attract the attention of many statisticians. There are a lot of good books on point processes and many of them contain chapters devoted to statistical inference for general and partic ular models of processes. There are even chapters on statistical estimation problems for inhomogeneous Poisson processes in asymptotic statements. Nevertheless it seems that the asymptotic theory of estimation for nonlinear models of Poisson processes needs some development. Here nonlinear means the models of inhomogeneous Pois son processes with intensity function nonlinearly depending on unknown parameters. In such situations the estimators usually cannot be written in exact form and are given as solutions of some equations. However the models can be quite fruitful in en gineering problems and the existing computing algorithms are sufficiently powerful to calculate these estimators. Therefore the properties of estimators can be interesting too.

An Introduction to Stochastic Processes and Their Applications

Petar Todorovic

Author : Petar Todorovic
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461397427

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An Introduction to Stochastic Processes and Their Applications by Petar Todorovic Pdf

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.

Introduction to Probability and Stochastic Processes with Applications

Liliana Blanco Castañeda,Viswanathan Arunachalam,Selvamuthu Dharmaraja

Author : Liliana Blanco Castañeda,Viswanathan Arunachalam,Selvamuthu Dharmaraja
Publisher : John Wiley & Sons
Page : 741 pages
File Size : 55,8 Mb
Release : 2014-08-21
Category : Mathematics
ISBN : 9781118344965

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Introduction to Probability and Stochastic Processes with Applications by Liliana Blanco Castañeda,Viswanathan Arunachalam,Selvamuthu Dharmaraja Pdf

An easily accessible, real-world approach to probability and stochastic processes Introduction to Probability and Stochastic Processes with Applications presents a clear, easy-to-understand treatment of probability and stochastic processes, providing readers with a solid foundation they can build upon throughout their careers. With an emphasis on applications in engineering, applied sciences, business and finance, statistics, mathematics, and operations research, the book features numerous real-world examples that illustrate how random phenomena occur in nature and how to use probabilistic techniques to accurately model these phenomena. The authors discuss a broad range of topics, from the basic concepts of probability to advanced topics for further study, including Itô integrals, martingales, and sigma algebras. Additional topical coverage includes: Distributions of discrete and continuous random variables frequently used in applications Random vectors, conditional probability, expectation, and multivariate normal distributions The laws of large numbers, limit theorems, and convergence of sequences of random variables Stochastic processes and related applications, particularly in queueing systems Financial mathematics, including pricing methods such as risk-neutral valuation and the Black-Scholes formula Extensive appendices containing a review of the requisite mathematics and tables of standard distributions for use in applications are provided, and plentiful exercises, problems, and solutions are found throughout. Also, a related website features additional exercises with solutions and supplementary material for classroom use. Introduction to Probability and Stochastic Processes with Applications is an ideal book for probability courses at the upper-undergraduate level. The book is also a valuable reference for researchers and practitioners in the fields of engineering, operations research, and computer science who conduct data analysis to make decisions in their everyday work.

An Introduction to Stochastic Modeling

Mark Pinsky,Samuel Karlin

Author : Mark Pinsky,Samuel Karlin
Publisher : Academic Press
Page : 585 pages
File Size : 55,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780123814166

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An Introduction to Stochastic Modeling by Mark Pinsky,Samuel Karlin Pdf

Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, Fourth Edition, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems. New to this edition: Realistic applications from a variety of disciplines integrated throughout the text, including more biological applications Plentiful, completely updated problems Completely updated and reorganized end-of-chapter exercise sets, 250 exercises with answers New chapters of stochastic differential equations and Brownian motion and related processes Additional sections on Martingale and Poisson process Realistic applications from a variety of disciplines integrated throughout the text Extensive end of chapter exercises sets, 250 with answers Chapter 1-9 of the new edition are identical to the previous edition New! Chapter 10 - Random Evolutions New! Chapter 11- Characteristic functions and Their Applications

Introduction to Probability with Statistical Applications

Géza Schay

Author : Géza Schay
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 45,7 Mb
Release : 2007-08-23
Category : Mathematics
ISBN : 9780817644970

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Introduction to Probability with Statistical Applications by Géza Schay Pdf

Introduction to Probability with Statistical Applications targets non-mathematics students, undergraduates and graduates, who do not need an exhaustive treatment of the subject. The presentation is rigorous and contains theorems and proofs, and linear algebra is largely avoided so only a minimal amount of multivariable calculus is needed. The book contains clear definitions, simplified notation and techniques of statistical analysis, which combined with well-chosen examples and exercises, motivate the exposition. Theory and applications are carefully balanced. Throughout the book there are references to more advanced concepts if required.

Stochastic Processes

Peter Watts Jones,Peter Smith

Author : Peter Watts Jones,Peter Smith
Publisher : CRC Press
Page : 255 pages
File Size : 42,5 Mb
Release : 2017-10-30
Category : Mathematics
ISBN : 9781498778121

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Stochastic Processes by Peter Watts Jones,Peter Smith Pdf

Based on a well-established and popular course taught by the authors over many years, Stochastic Processes: An Introduction, Third Edition, discusses the modelling and analysis of random experiments, where processes evolve over time. The text begins with a review of relevant fundamental probability. It then covers gambling problems, random walks, and Markov chains. The authors go on to discuss random processes continuous in time, including Poisson, birth and death processes, and general population models, and present an extended discussion on the analysis of associated stationary processes in queues. The book also explores reliability and other random processes, such as branching, martingales, and simple epidemics. A new chapter describing Brownian motion, where the outcomes are continuously observed over continuous time, is included. Further applications, worked examples and problems, and biographical details have been added to this edition. Much of the text has been reworked. The appendix contains key results in probability for reference. This concise, updated book makes the material accessible, highlighting simple applications and examples. A solutions manual with fully worked answers of all end-of-chapter problems, and Mathematica® and R programs illustrating many processes discussed in the book, can be downloaded from crcpress.com.

Lectures on the Poisson Process

Günter Last,Mathew Penrose

Author : Günter Last,Mathew Penrose
Publisher : Cambridge University Press
Page : 315 pages
File Size : 55,6 Mb
Release : 2017-10-26
Category : Mathematics
ISBN : 9781107088016

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Lectures on the Poisson Process by Günter Last,Mathew Penrose Pdf

A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.

An Introduction to Stochastic Modeling

Howard M. Taylor,Samuel Karlin

Author : Howard M. Taylor,Samuel Karlin
Publisher : Academic Press
Page : 579 pages
File Size : 53,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483220444

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An Introduction to Stochastic Modeling by Howard M. Taylor,Samuel Karlin Pdf

An Introduction to Stochastic Modeling, Revised Edition provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

Introduction to Stochastic Processes

Erhan Cinlar

Author : Erhan Cinlar
Publisher : Courier Corporation
Page : 418 pages
File Size : 45,8 Mb
Release : 2013-02-01
Category : Mathematics
ISBN : 9780486497976

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Introduction to Stochastic Processes by Erhan Cinlar Pdf

This clear presentation of themost fundamental models ofrandom phenomena employsmethods that recognize computerrelatedaspects of theory. Topicsinclude probability spaces andrandom variables, expectationsand independence, Bernoulliprocesses and sums of independentrandom variables, Poisson processes, Markov chainsand processes, and renewal theory. Assuming only a backgroundin calculus, this outstanding text includes an introductionto basic stochastic processes.Reprint of the Prentice-Hall Publishers, Englewood Cliffs,New Jersey, 1975 edition.

Elementary Applications of Probability Theory

Henry C. Tuckwell

Author : Henry C. Tuckwell
Publisher : Routledge
Page : 200 pages
File Size : 55,8 Mb
Release : 2018-02-06
Category : Mathematics
ISBN : 9781351452953

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Elementary Applications of Probability Theory by Henry C. Tuckwell Pdf

This book provides a clear and straightforward introduction to applications of probability theory with examples given in the biological sciences and engineering. The first chapter contains a summary of basic probability theory. Chapters two to five deal with random variables and their applications. Topics covered include geometric probability, estimation of animal and plant populations, reliability theory and computer simulation. Chapter six contains a lucid account of the convergence of sequences of random variables, with emphasis on the central limit theorem and the weak law of numbers. The next four chapters introduce random processes, including random walks and Markov chains illustrated by examples in population genetics and population growth. This edition also includes two chapters which introduce, in a manifestly readable fashion, the topic of stochastic differential equations and their applications.

Introduction to Statistical Process Control

Muhammad Aslam,Aamir Saghir,Liaquat Ahmad

Author : Muhammad Aslam,Aamir Saghir,Liaquat Ahmad
Publisher : John Wiley & Sons
Page : 288 pages
File Size : 49,6 Mb
Release : 2020-08-25
Category : Mathematics
ISBN : 9781119528432

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Introduction to Statistical Process Control by Muhammad Aslam,Aamir Saghir,Liaquat Ahmad Pdf

An Introduction to the Fundamentals and History of Control Charts, Applications, and Guidelines for Implementation Introduction to Statistical Process Control examines various types of control charts that are typically used by engineering students and practitioners. This book helps readers develop a better understanding of the history, implementation, and use-cases. Students are presented with varying control chart techniques, information, and roadmaps to ensure their control charts are operating efficiently and producing specification-confirming products. This is the essential text on the theories and applications behind statistical methods and control procedures. This eight-chapter reference breaks information down into digestible sections and covers topics including: ● An introduction to the basics as well as a background of control charts ● Widely used and newly researched attributes of control charts, including guidelines for implementation ● The process capability index for both normal and non-normal distribution via the sampling of multiple dependent states ● An overview of attribute control charts based on memory statistics ● The development of control charts using EQMA statistics For a solid understanding of control methodologies and the basics of quality assurance, Introduction to Statistical Process Control is a definitive reference designed to be read by practitioners and students alike. It is an essential textbook for those who want to explore quality control and systems design.

Stochastic Analysis for Poisson Point Processes

Giovanni Peccati,Matthias Reitzner

Author : Giovanni Peccati,Matthias Reitzner
Publisher : Springer
Page : 346 pages
File Size : 41,9 Mb
Release : 2016-07-07
Category : Mathematics
ISBN : 9783319052335

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Stochastic Analysis for Poisson Point Processes by Giovanni Peccati,Matthias Reitzner Pdf

Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years – due mainly to the impetus of the authors and their collaborators – a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects. This unique book presents an organic collection of authoritative surveys written by the principal actors in this rapidly evolving field, offering a rigorous yet lively presentation of its many facets.

Poisson Point Processes

Roy L. Streit

Author : Roy L. Streit
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 48,8 Mb
Release : 2010-09-15
Category : Technology & Engineering
ISBN : 9781441969231

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Poisson Point Processes by Roy L. Streit Pdf

"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.

An Introduction to the Theory of Point Processes

D.J. Daley,D. Vere-Jones

Author : D.J. Daley,D. Vere-Jones
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 55,7 Mb
Release : 2006-04-10
Category : Mathematics
ISBN : 9780387215648

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An Introduction to the Theory of Point Processes by D.J. Daley,D. Vere-Jones Pdf

Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure. Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text.

Introduction To The Statistics Of Poisson Processes And Applications

Introduction to the Statistics of Poisson Processes and Applications by Yury A. Kutoyants Pdf

Statistical Inference for Spatial Poisson Processes by Yu A. Kutoyants Pdf

An Introduction to Stochastic Processes and Their Applications by Petar Todorovic Pdf

Introduction to Probability and Stochastic Processes with Applications by Liliana Blanco Castañeda,Viswanathan Arunachalam,Selvamuthu Dharmaraja Pdf

An Introduction to Stochastic Modeling by Mark Pinsky,Samuel Karlin Pdf

Introduction to Probability with Statistical Applications by Géza Schay Pdf

Stochastic Processes by Peter Watts Jones,Peter Smith Pdf

Lectures on the Poisson Process by Günter Last,Mathew Penrose Pdf

An Introduction to Stochastic Modeling by Howard M. Taylor,Samuel Karlin Pdf

Introduction to Stochastic Processes by Erhan Cinlar Pdf

Elementary Applications of Probability Theory by Henry C. Tuckwell Pdf

Introduction to Statistical Process Control by Muhammad Aslam,Aamir Saghir,Liaquat Ahmad Pdf

Stochastic Analysis for Poisson Point Processes by Giovanni Peccati,Matthias Reitzner Pdf

Poisson Point Processes by Roy L. Streit Pdf

An Introduction to the Theory of Point Processes by D.J. Daley,D. Vere-Jones Pdf

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