Renewal Processes

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Compound Renewal Processes

A. A. Borovkov
Compound Renewal Processes Book PDF

Author : A. A. Borovkov
Publisher : Cambridge University Press
Page : 128 pages
File Size : 46,9 Mb
Release : 2022-06-30
Category : Mathematics
ISBN : 9781009115605

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Compound Renewal Processes by A. A. Borovkov Pdf

Compound renewal processes (CRPs) are among the most ubiquitous models arising in applications of probability. At the same time, they are a natural generalization of random walks, the most well-studied classical objects in probability theory. This monograph, written for researchers and graduate students, presents the general asymptotic theory and generalizes many well-known results concerning random walks. The book contains the key limit theorems for CRPs, functional limit theorems, integro-local limit theorems, large and moderately large deviation principles for CRPs in the state space and in the space of trajectories, including large deviation principles in boundary crossing problems for CRPs, with an explicit form of the rate functionals, and an extension of the invariance principle for CRPs to the domain of moderately large and small deviations. Applications establish the key limit laws for Markov additive processes, including limit theorems in the domains of normal and large deviations.

Uncertain Renewal Processes

Kai Yao
Uncertain Renewal Processes Book PDF

Author : Kai Yao
Publisher : Springer
Page : 156 pages
File Size : 51,5 Mb
Release : 2019-07-31
Category : Mathematics
ISBN : 9789811393457

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Uncertain Renewal Processes by Kai Yao Pdf

This book explores various renewal processes in the context of probability theory, uncertainty theory and chance theory. It also covers the applications of these renewal processes in maintenance models and insurance risk models. The methods used to derive the limit of the renewal rate, the reward rate, and the availability rate are of particular interest, as they can easily be extended to the derivation of other models. Its comprehensive and systematic treatment of renewal processes, renewal reward processes and the alternating renewal process is one of the book’s major features, making it particularly valuable for readers who are interested in learning about renewal theory. Given its scope, the book will benefit researchers, engineers, and graduate students in the fields of mathematics, information science, operations research, industrial engineering, etc.

Basics of Applied Stochastic Processes

Richard Serfozo
Basics of Applied Stochastic Processes Book PDF

Author : Richard Serfozo
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 43,6 Mb
Release : 2009-01-24
Category : Mathematics
ISBN : 9783540893325

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Basics of Applied Stochastic Processes by Richard Serfozo Pdf

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.

Point Processes for Reliability Analysis

Ji Hwan Cha,Maxim Finkelstein
Point Processes for Reliability Analysis Book PDF

Author : Ji Hwan Cha,Maxim Finkelstein
Publisher : Springer
Page : 419 pages
File Size : 54,8 Mb
Release : 2018-01-17
Category : Technology & Engineering
ISBN : 9783319735405

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Point Processes for Reliability Analysis by Ji Hwan Cha,Maxim Finkelstein Pdf

Focusing on the theory and applications of point processes, Point Processes for Reliability Analysis naturally combines classical results on the basic and advanced properties of point processes with recent theoretical findings of the authors. It also presents numerous examples that illustrate how general results and approaches are applied to stochastic description of repairable systems and systems operating in a random environment modelled by shock processes. The real life objects are operating in a changing, random environment. One of the ways to model an impact of this environment is via the external shocks occurring in accordance with some stochastic point processes. The Poisson (homogeneous and nonhomogeneous) process, the renewal process and their generalizations are considered as models for external shocks affecting an operating system. At the same time these processes model the consecutive failure/repair times of repairable engineering systems. Perfect, minimal and intermediate (imperfect) repairs are discussed in this respect. Covering material previously available only in the journal literature, Point Processes for Reliability Analysis provides a survey of recent developments in this area which will be invaluable to researchers and advanced students in reliability engineering and applied mathematics.

Renewal Processes

Kosto V. Mitov,Edward Omey
Renewal Processes Book PDF

Author : Kosto V. Mitov,Edward Omey
Publisher : Springer Science & Business
Page : 128 pages
File Size : 44,6 Mb
Release : 2014-04-23
Category : Mathematics
ISBN : 9783319058559

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Renewal Processes by Kosto V. Mitov,Edward Omey Pdf

This monograph serves as an introductory text to classical renewal theory and some of its applications for graduate students and researchers in mathematics and probability theory. Renewal processes play an important part in modeling many phenomena in insurance, finance, queuing systems, inventory control and other areas. In this book, an overview of univariate renewal theory is given and renewal processes in the non-lattice and lattice case are discussed. A pre-requisite is a basic knowledge of probability theory.

Stochastic Processes: Theory and Methods

D N Shanbhag,Calyampudi Radhakrishna Rao
Stochastic Processes Theory and Methods Book PDF

Author : D N Shanbhag,Calyampudi Radhakrishna Rao
Publisher : Gulf Professional Publishing
Page : 990 pages
File Size : 51,9 Mb
Release : 2001
Category : Mathematics
ISBN : 0444500146

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Stochastic Processes: Theory and Methods by D N Shanbhag,Calyampudi Radhakrishna Rao Pdf

This volume in the series contains chapters on areas such as pareto processes, branching processes, inference in stochastic processes, Poisson approximation, Levy processes, and iterated random maps and some classes of Markov processes. Other chapters cover random walk and fluctuation theory, a semigroup representation and asymptomatic behavior of certain statistics of the Fisher-Wright-Moran coalescent, continuous-time ARMA processes, record sequence and their applications, stochastic networks with product form equilibrium, and stochastic processes in insurance and finance. Other subjects include renewal theory, stochastic processes in reliability, supports of stochastic processes of multiplicity one, Markov chains, diffusion processes, and Ito's stochastic calculus and its applications. c. Book News Inc.

Stochastic Processes and Their Applications

Frank Beichelt,L. Paul Fatti
Stochastic Processes and Their Applications Book PDF

Author : Frank Beichelt,L. Paul Fatti
Publisher : CRC Press
Page : 342 pages
File Size : 51,9 Mb
Release : 2001-10-18
Category : Mathematics
ISBN : 0415272327

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Stochastic Processes and Their Applications by Frank Beichelt,L. Paul Fatti Pdf

This book introduces stochastic processes and their applications for students in engineering, industrial statistics, science, operations research, business, and finance. It provides the theoretical foundations for modeling time-dependent random phenomena encountered in these disciplines. Through numerous science and engineering-based examples and exercises, the author presents the subject in a comprehensible, practically oriented way, but he also includes some important proofs and theoretically challenging examples and exercises that will appeal to more mathematically minded readers. Solutions to most of the exercises are included either in an appendix or within the text.

Adventures in Stochastic Processes

Sidney I. Resnick
Adventures in Stochastic Processes Book PDF

Author : Sidney I. Resnick
Publisher : Springer Science & Business Media
Page : 640 pages
File Size : 50,5 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781461203872

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Adventures in Stochastic Processes by Sidney I. Resnick Pdf

Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time varying randomness. This text offers easy access to this fundamental topic for many students of applied sciences at many levels. It includes examples, exercises, applications, and computational procedures. It is uniquely useful for beginners and non-beginners in the field. No knowledge of measure theory is presumed.

Stochastic Models in Operations Research

Daniel P. Heyman,Matthew J. Sobel
Stochastic Models in Operations Research Book PDF

Author : Daniel P. Heyman,Matthew J. Sobel
Publisher : Courier Corporation
Page : 564 pages
File Size : 41,9 Mb
Release : 2004-01-01
Category : Mathematics
ISBN : 0486432599

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Stochastic Models in Operations Research by Daniel P. Heyman,Matthew J. Sobel Pdf

This volume of a 2-volume set explores the central facts and ideas of stochastic processes, illustrating their use in models based on applied and theoretical investigations. Explores stochastic processes, operating characteristics of stochastic systems, and stochastic optimization. Comprehensive in its scope, this graduate-level text emphasizes the practical importance, intellectual stimulation, and mathematical elegance of stochastic models.

Introduction to Stochastic Processes Using R

Sivaprasad Madhira,Shailaja Deshmukh
Introduction to Stochastic Processes Using R Book PDF

Author : Sivaprasad Madhira,Shailaja Deshmukh
Publisher : Springer Nature
Page : 663 pages
File Size : 55,8 Mb
Release : 2023-12-05
Category : Business & Economics
ISBN : 9789819956012

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Introduction to Stochastic Processes Using R by Sivaprasad Madhira,Shailaja Deshmukh Pdf

This textbook presents some basic stochastic processes, mainly Markov processes. It begins with a brief introduction to the framework of stochastic processes followed by the thorough discussion on Markov chains, which is the simplest and the most important class of stochastic processes. The book then elaborates the theory of Markov chains in detail including classification of states, the first passage distribution, the concept of periodicity and the limiting behaviour of a Markov chain in terms of associated stationary and long run distributions. The book first illustrates the theory for some typical Markov chains, such as random walk, gambler's ruin problem, Ehrenfest model and Bienayme-Galton-Watson branching process; and then extends the discussion when time parameter is continuous. It presents some important examples of a continuous time Markov chain, which include Poisson process, birth process, death process, birth and death processes and their variations. These processes play a fundamental role in the theory and applications in queuing and inventory models, population growth, epidemiology and engineering systems. The book studies in detail the Poisson process, which is the most frequently applied stochastic process in a variety of fields, with its extension to a renewal process. The book also presents important basic concepts on Brownian motion process, a stochastic process of historic importance. It covers its few extensions and variations, such as Brownian bridge, geometric Brownian motion process, which have applications in finance, stock markets, inventory etc. The book is designed primarily to serve as a textbook for a one semester introductory course in stochastic processes, in a post-graduate program, such as Statistics, Mathematics, Data Science and Finance. It can also be used for relevant courses in other disciplines. Additionally, it provides sufficient background material for studying inference in stochastic processes. The book thus fulfils the need of a concise but clear and student-friendly introduction to various types of stochastic processes.

Discrete Stochastic Processes

Robert G. Gallager
Discrete Stochastic Processes Book PDF

Author : Robert G. Gallager
Publisher : Springer Science & Business Media
Page : 280 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461523291

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Discrete Stochastic Processes by Robert G. Gallager Pdf

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.

An Introduction to the Theory of Point Processes

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

Author : D.J. Daley,D. Vere-Jones
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 49,7 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.

Applied Stochastic Processes

Ming Liao
Applied Stochastic Processes Book PDF

Author : Ming Liao
Publisher : CRC Press
Page : 209 pages
File Size : 41,9 Mb
Release : 2013-07-22
Category : Business & Economics
ISBN : 9781466589339

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Applied Stochastic Processes by Ming Liao Pdf

Applied Stochastic Processes presents a concise, graduate-level treatment of the subject, emphasizing applications and practical computation. It also establishes the complete mathematical theory in an accessible way. After reviewing basic probability, the text covers Poisson processes, renewal processes, discrete- and continuous-time Markov chains, and Brownian motion. It also offers an introduction to stochastic differential equations. While the main applications described are queues, the book also considers other examples, such as the mathematical model of a single stock market. With exercises in most sections, this book provides a clear, practical introduction for beginning graduate students. The material is presented in a straightforward manner using short, motivating examples. In addition, the author develops the mathematical theory with a strong emphasis on probability intuition.

Stochastic Processes

Robert G. Gallager
Stochastic Processes Book PDF

Author : Robert G. Gallager
Publisher : Cambridge University Press
Page : 559 pages
File Size : 53,9 Mb
Release : 2013-12-12
Category : Technology & Engineering
ISBN : 9781107435315

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Stochastic Processes by Robert G. Gallager Pdf

This definitive textbook provides a solid introduction to discrete and continuous stochastic processes, tackling a complex field in a way that instils a deep understanding of the relevant mathematical principles, and develops an intuitive grasp of the way these principles can be applied to modelling real-world systems. It includes a careful review of elementary probability and detailed coverage of Poisson, Gaussian and Markov processes with richly varied queuing applications. The theory and applications of inference, hypothesis testing, estimation, random walks, large deviations, martingales and investments are developed. Written by one of the world's leading information theorists, evolving over twenty years of graduate classroom teaching and enriched by over 300 exercises, this is an exceptional resource for anyone looking to develop their understanding of stochastic processes.

Stochastic Processes and their Applications

M.J. Beckmann,M.N. Gopalan,R. Subramanian
Stochastic Processes and their Applications Book PDF

Author : M.J. Beckmann,M.N. Gopalan,R. Subramanian
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642582011

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Stochastic Processes and their Applications by M.J. Beckmann,M.N. Gopalan,R. Subramanian Pdf

A volume of this nature containing a collection of papers has been brought out to honour a gentleman - a friend and a colleague - whose work has, to a large extent, advanced and popularized the use of stochastic point processes. Professor Srinivasan celebrated his sixt~ first 1:!irth d~ on December 16,1990 and will be retiring as Professor of Applied Mathematics from the Indian Institute of Technolo~, Madras on June 30,1991. In view of his outstanding contributions to the theor~ and applications of stochastic processes over a time span of thirt~ ~ears, it seemed appropriate not to let his birth d~ and retirement pass unnoticed. A s~posium in his honour and the publication of the proceedings appeared to us to be the most natural and sui table ~ to mark the occasion. The Indian Societ~ for ProbabU it~ and Statistics volunteered to organize the S~posium as part of their XII Annual conference in Bomba~. We requested a number of long-time friends, colleagues and former students of Professor Srinivasan to contribute a paper preferabl~ in the area of stochastic processes and their applications. The positive response and the enthusiastic cooperation of these distinguished scientists have resulted in the present collection. The contributions to this volume are divided into four parts: Stochastic Theor~ (2 articles), P~sics (6 articles), Biolo~ (4 articles) and Operations Research (12 articles). In addition the ke~note address delivered b~ Professor Srinivasan in the S~posium is also included.