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Continuous-Time Markov Chains

Author : William J. Anderson

Publisher : Springer Science & Business Media

Page : 367 pages

File Size : 25,13 MB

Release : 2012-12-06

Category : Mathematics

ISBN : 1461230381

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Book Description

Continuous time parameter Markov chains have been useful for modeling various random phenomena occurring in queueing theory, genetics, demography, epidemiology, and competing populations. This is the first book about those aspects of the theory of continuous time Markov chains which are useful in applications to such areas. It studies continuous time Markov chains through the transition function and corresponding q-matrix, rather than sample paths. An extensive discussion of birth and death processes, including the Stieltjes moment problem, and the Karlin-McGregor method of solution of the birth and death processes and multidimensional population processes is included, and there is an extensive bibliography. Virtually all of this material is appearing in book form for the first time.



Continuous-Time Markov Chains and Applications

Author : George G. Yin

Publisher : Springer

Page : 358 pages

File Size : 15,85 MB

Release : 2012-12-06

Category : Mathematics

ISBN : 1461206278

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Book Description

Using a singular perturbation approach, this is a systematic treatment of those systems that naturally arise in queuing theory, control and optimisation, and manufacturing, gathering a number of ideas which were previously scattered throughout the literature. The book presents results on asymptotic expansions of the corresponding probability distributions, functional occupation measures, exponential upper bounds, and asymptotic normality. To bridge the gap between theory and applications, a large portion of the book is devoted to various applications, thus reducing the dimensionality for problems under Markovian disturbances and providing tools for dealing with large-scale and complex real-world situations. Much of this stems from the authors'recent research, presenting results which have not appeared elsewhere. An important reference for researchers in applied mathematics, probability and stochastic processes, operations research, control theory, and optimisation.



Continuous Time Markov Processes

Author : Thomas Milton Liggett

Publisher : American Mathematical Soc.

Page : 290 pages

File Size : 22,99 MB

Release : 2010

Category : Mathematics

ISBN : 0821849492

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Book Description

Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes, and applies this theory to various special examples.



Markov Chains

Author : Pierre Bremaud

Publisher : Springer Science & Business Media

Page : 456 pages

File Size : 11,55 MB

Release : 2013-03-09

Category : Mathematics

ISBN : 1475731248

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Book Description

Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic modelling. However it is motivated by significant applications and progressively brings the student to the borders of contemporary research. Examples are from a wide range of domains, including operations research and electrical engineering. Researchers and students in these areas as well as in physics, biology and the social sciences will find this book of interest.



Continuous-Time Markov Decision Processes

Author : Xianping Guo

Publisher : Springer Science & Business Media

Page : 240 pages

File Size : 41,1 MB

Release : 2009-09-18

Category : Mathematics

ISBN : 3642025471

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Book Description

Continuous-time Markov decision processes (MDPs), also known as controlled Markov chains, are used for modeling decision-making problems that arise in operations research (for instance, inventory, manufacturing, and queueing systems), computer science, communications engineering, control of populations (such as fisheries and epidemics), and management science, among many other fields. This volume provides a unified, systematic, self-contained presentation of recent developments on the theory and applications of continuous-time MDPs. The MDPs in this volume include most of the cases that arise in applications, because they allow unbounded transition and reward/cost rates. Much of the material appears for the first time in book form.



Sensitivity Analysis: Matrix Methods in Demography and Ecology

Author : Hal Caswell

Publisher : Springer

Page : 308 pages

File Size : 21,56 MB

Release : 2019-04-02

Category : Social Science

ISBN : 3030105342

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Book Description

This open access book shows how to use sensitivity analysis in demography. It presents new methods for individuals, cohorts, and populations, with applications to humans, other animals, and plants. The analyses are based on matrix formulations of age-classified, stage-classified, and multistate population models. Methods are presented for linear and nonlinear, deterministic and stochastic, and time-invariant and time-varying cases. Readers will discover results on the sensitivity of statistics of longevity, life disparity, occupancy times, the net reproductive rate, and statistics of Markov chain models in demography. They will also see applications of sensitivity analysis to population growth rates, stable population structures, reproductive value, equilibria under immigration and nonlinearity, and population cycles. Individual stochasticity is a theme throughout, with a focus that goes beyond expected values to include variances in demographic outcomes. The calculations are easily and accurately implemented in matrix-oriented programming languages such as Matlab or R. Sensitivity analysis will help readers create models to predict the effect of future changes, to evaluate policy effects, and to identify possible evolutionary responses to the environment. Complete with many examples of the application, the book will be of interest to researchers and graduate students in human demography and population biology. The material will also appeal to those in mathematical biology and applied mathematics.



Introduction to Probability Models

Author : Sheldon M. Ross

Publisher : Academic Press

Page : 801 pages

File Size : 10,30 MB

Release : 2006-12-11

Category : Mathematics

ISBN : 0123756871

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Book Description

Introduction to Probability Models, Tenth Edition, provides an introduction to elementary probability theory and stochastic processes. There are two approaches to the study of probability theory. One is heuristic and nonrigorous, and attempts to develop in students an intuitive feel for the subject that enables him or her to think probabilistically. The other approach attempts a rigorous development of probability by using the tools of measure theory. The first approach is employed in this text. The book begins by introducing basic concepts of probability theory, such as the random variable, conditional probability, and conditional expectation. This is followed by discussions of stochastic processes, including Markov chains and Poison processes. The remaining chapters cover queuing, reliability theory, Brownian motion, and simulation. Many examples are worked out throughout the text, along with exercises to be solved by students. This book will be particularly useful to those interested in learning how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. Ideally, this text would be used in a one-year course in probability models, or a one-semester course in introductory probability theory or a course in elementary stochastic processes. New to this Edition: 65% new chapter material including coverage of finite capacity queues, insurance risk models and Markov chains Contains compulsory material for new Exam 3 of the Society of Actuaries containing several sections in the new exams Updated data, and a list of commonly used notations and equations, a robust ancillary package, including a ISM, SSM, and test bank Includes SPSS PASW Modeler and SAS JMP software packages which are widely used in the field Hallmark features: Superior writing style Excellent exercises and examples covering the wide breadth of coverage of probability topics Real-world applications in engineering, science, business and economics



Design and Analysis of Biomolecular Circuits

Author : Heinz Koeppl

Publisher : Springer Science & Business Media

Page : 407 pages

File Size : 11,14 MB

Release : 2011-05-21

Category : Technology & Engineering

ISBN : 1441967664

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Book Description

The book deals with engineering aspects of the two emerging and intertwined fields of synthetic and systems biology. Both fields hold promise to revolutionize the way molecular biology research is done, the way today’s drug discovery works and the way bio-engineering is done. Both fields stress the importance of building and characterizing small bio-molecular networks in order to synthesize incrementally and understand large complex networks inside living cells. Reminiscent of computer-aided design (CAD) of electronic circuits, abstraction is believed to be the key concept to achieve this goal. It allows hiding the overwhelming complexity of cellular processes by encapsulating network parts into abstract modules. This book provides a unique perspective on how concepts and methods from CAD of electronic circuits can be leveraged to overcome complexity barrier perceived in synthetic and systems biology.



Reliability and Availability Engineering

Author : Kishor S. Trivedi

Publisher : Cambridge University Press

Page : 729 pages

File Size : 47,5 MB

Release : 2017-08-03

Category : Computers

ISBN : 1107099501

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Book Description

Learn about the techniques used for evaluating the reliability and availability of engineered systems with this comprehensive guide.



Probability Theory and Stochastic Processes

Author : Pierre Brémaud

Publisher : Springer Nature

Page : 713 pages

File Size : 49,53 MB

Release : 2020-04-07

Category : Mathematics

ISBN : 3030401839

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Book Description

The ultimate objective of this book is to present a panoramic view of the main stochastic processes which have an impact on applications, with complete proofs and exercises. Random processes play a central role in the applied sciences, including operations research, insurance, finance, biology, physics, computer and communications networks, and signal processing. In order to help the reader to reach a level of technical autonomy sufficient to understand the presented models, this book includes a reasonable dose of probability theory. On the other hand, the study of stochastic processes gives an opportunity to apply the main theoretical results of probability theory beyond classroom examples and in a non-trivial manner that makes this discipline look more attractive to the applications-oriented student. One can distinguish three parts of this book. The first four chapters are about probability theory, Chapters 5 to 8 concern random sequences, or discrete-time stochastic processes, and the rest of the book focuses on stochastic processes and point processes. There is sufficient modularity for the instructor or the self-teaching reader to design a course or a study program adapted to her/his specific needs. This book is in a large measure self-contained.