[PDF] Renewal Processes eBook

Author : A. A. Borovkov
Publisher : Cambridge University Press
Page : pages
File Size : 23,15 MB
Release : 2022-06-30
Category : Mathematics
ISBN : 100911560X

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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.

Author : Kai Yao
Publisher : Springer
Page : 156 pages
File Size : 10,34 MB
Release : 2019-07-31
Category : Mathematics
ISBN : 9811393451

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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.

Author : Kosto V. Mitov
Publisher : Springer Science & Business
Page : 128 pages
File Size : 49,19 MB
Release : 2014-04-23
Category : Mathematics
ISBN : 331905855X

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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.

Author : Richard Serfozo
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 42,45 MB
Release : 2009-01-24
Category : Mathematics
ISBN : 3540893326

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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.

Author : David R. Cox
Publisher : Chapman and Hall/CRC
Page : 164 pages
File Size : 28,58 MB
Release : 1967-09
Category : Juvenile Nonfiction
ISBN :

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Renewal theory arose from the study of 'self-renewing aggregates' and has developed into the investigation of some general results in probability theory connected with sums of independent non-negative random variables.

Author : Rolf A. Lundin
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 43,55 MB
Release : 2012-12-06
Category : Business & Economics
ISBN : 1461556910

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There is a growing tendency to organize various aspects of business life by projects, and to set up temporary organizations in a competition where speed and adaptability becomes a major necessity. Organizing by projects is perceived as a good way to ensure action and to stress the importance of getting work done. However, there is a need to balance the stress on action so that learning capabilities are not only retained, but augmented. Projects as Arenas for Renewal and Learning Processes provides examples of how different types of projects function from a learning or renewal perspective, taken from a wide variety of real-life environments in industrial and public organizations. This book illustrates the mistaken habit of assuming too much in the project area: for example, project notions are, in fact, culture-dependent; classical market-oriented contracting business relations do not fit with the learning dimension of projects; and long-term learning on core competencies and product development projects need to be connected. The book is also intended to represent many of the research frontiers in the project field. Enhancing learning capabilities is - or should be - of a mutual concern to researchers and managers alike.

Author : D N Shanbhag
Publisher : Gulf Professional Publishing
Page : 990 pages
File Size : 26,75 MB
Release : 2001
Category : Mathematics
ISBN : 9780444500144

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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.

Author : Randolph Nelson
Publisher : Springer Science & Business Media
Page : 595 pages
File Size : 17,95 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 1475724268

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We will occasionally footnote a portion of text with a "**,, to indicate Notes on the that this portion can be initially bypassed. The reasons for bypassing a Text portion of the text include: the subject is a special topic that will not be referenced later, the material can be skipped on first reading, or the level of mathematics is higher than the rest of the text. In cases where a topic is self-contained, we opt to collect the material into an appendix that can be read by students at their leisure. The material in the text cannot be fully assimilated until one makes it Notes on "their own" by applying the material to specific problems. Self-discovery Problems is the best teacher and although they are no substitute for an inquiring mind, problems that explore the subject from different viewpoints can often help the student to think about the material in a uniquely per sonal way. With this in mind, we have made problems an integral part of this work and have attempted to make them interesting as well as informative.

Author : Pavel Petrovich Bocharov
Publisher : Walter de Gruyter
Page : 468 pages
File Size : 30,16 MB
Release : 2004
Category : Architecture
ISBN : 9789067643986

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The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.

Author : Robert G. Gallager
Publisher : Cambridge University Press
Page : 559 pages
File Size : 16,63 MB
Release : 2013-12-12
Category : Technology & Engineering
ISBN : 1107435315

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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.