Introduction To Markov Chains
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Introduction To Markov Chains
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Author : Ehrhard Behrends
language : en
Publisher: Vieweg+Teubner Verlag
Release Date : 2014-07-08
Introduction To Markov Chains written by Ehrhard Behrends and has been published by Vieweg+Teubner Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-08 with Mathematics categories.
Besides the investigation of general chains the book contains chapters which are concerned with eigenvalue techniques, conductance, stopping times, the strong Markov property, couplings, strong uniform times, Markov chains on arbitrary finite groups (including a crash-course in harmonic analysis), random generation and counting, Markov random fields, Gibbs fields, the Metropolis sampler, and simulated annealing. With 170 exercises.
An Introduction To Markov Chain Analysis
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Author : Lyndhurst Collins
language : en
Publisher: Geo Abstracts Limited
Release Date : 1975
An Introduction To Markov Chain Analysis written by Lyndhurst Collins and has been published by Geo Abstracts Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
An Introduction To Markov Chain Analysis
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Author : L. C. Collins
language : en
Publisher:
Release Date : 1975
An Introduction To Markov Chain Analysis written by L. C. Collins and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
Understanding Markov Chains
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Author : Nicolas Privault
language : en
Publisher: Springer
Release Date : 2018-08-03
Understanding Markov Chains written by Nicolas Privault and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-03 with Mathematics categories.
This book provides an undergraduate-level introduction to discrete and continuous-time Markov chains and their applications, with a particular focus on the first step analysis technique and its applications to average hitting times and ruin probabilities. It also discusses classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes. It first examines in detail two important examples (gambling processes and random walks) before presenting the general theory itself in the subsequent chapters. It also provides an introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times, together with a chapter on spatial Poisson processes. The concepts presented are illustrated by examples, 138 exercises and 9 problems with their solutions.
Continuous Time Markov Processes
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Author : Thomas M. Liggett
language : en
Publisher: American Mathematical Society
Release Date : 2025-08-27
Continuous Time Markov Processes written by Thomas M. Liggett and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-27 with Mathematics categories.
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. The initial chapter is devoted to the most important classical example?one-dimensional Brownian motion. This, together with a chapter on continuous time Markov chains, provides the motivation for the general setup based on semigroups and generators. Chapters on stochastic calculus and probabilistic potential theory give an introduction to some of the key areas of application of Brownian motion and its relatives. A chapter on interacting particle systems treats a more recently developed class of Markov processes that have as their origin problems in physics and biology. This is a textbook for a graduate course that can follow one that covers basic probabilistic limit theorems and discrete time processes.
Introduction To Markov Chains
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Author : D. Dawson
language : fr
Publisher:
Release Date : 1970
Introduction To Markov Chains written by D. Dawson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.
An Introduction To Markov Processes
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Author : Daniel W. Stroock
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-10-14
An Introduction To Markov Processes written by Daniel W. Stroock 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 2005-10-14 with Mathematics categories.
To some extent, it would be accurate to summarize the contents of this book as an intolerably protracted description of what happens when either one raises a transition probability matrix P (i. e. , all entries (P)»j are n- negative and each row of P sums to 1) to higher and higher powers or one exponentiates R(P — I), where R is a diagonal matrix with non-negative entries. Indeed, when it comes right down to it, that is all that is done in this book. However, I, and others of my ilk, would take offense at such a dismissive characterization of the theory of Markov chains and processes with values in a countable state space, and a primary goal of mine in writing this book was to convince its readers that our offense would be warranted. The reason why I, and others of my persuasion, refuse to consider the theory here as no more than a subset of matrix theory is that to do so is to ignore the pervasive role that probability plays throughout. Namely, probability theory provides a model which both motivates and provides a context for what we are doing with these matrices. To wit, even the term "transition probability matrix" lends meaning to an otherwise rather peculiar set of hypotheses to make about a matrix.
Markov Models
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Author : Joshua Chapmann
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2017-10-29
Markov Models written by Joshua Chapmann and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-29 with Markov processes categories.
What is a MEMORYLESS predictive model? Markov models are a powerful predictive technique used to model stochastic systems using time-series data. They are centered around the fundamental property of "memorylessness," stating that the outcome of a problem depends only on the current state of the system - historical data must be ignored. This model construction may sound overly simplistic. After all, if you have historical data why not use it to develop more complete and well-informed models? Surely, it would lead to more accurate predictions. However, when modelling time-series data where previous results are of limited relevance, a memoryless model delivers vast performance advantages. By considering only the present state, algorithms become highly scalable, stable, fast and, above-all-else, extremely versatile. Speech recognition is a perfect example - nearly all of today's speech recognition algorthms are built using Markov Models. In this book we will explore why a Memoryless predictive model can be so advantageous to the modern tech industry. We will take a look at fundamental mathematics and high-level concepts alike, extending our understanding of the subject beyond the simple Markov Model. You will learn... Foundations of Markov Models Markov Chains Case Study: Google PageRank Hidden Markov Models Bayesian Networks Inference Tasks
Performance Modeling Of Communication Networks With Markov Chains
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Author : Jeonghoon Mo
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Performance Modeling Of Communication Networks With Markov Chains written by Jeonghoon Mo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Computers categories.
This book is an introduction to Markov chain modeling with applications to communication networks. It begins with a general introduction to performance modeling in Chapter 1 where we introduce different performance models. We then introduce basic ideas of Markov chain modeling: Markov property, discrete time Markov chain (DTMC) and continuous time Markov chain (CTMC). We also discuss how to find the steady state distributions from these Markov chains and how they can be used to compute the system performance metric. The solution methodologies include a balance equation technique, limiting probability technique, and the uniformization. We try to minimize the theoretical aspects of the Markov chain so that the book is easily accessible to readers without deep mathematical backgrounds. We then introduce how to develop a Markov chain model with simple applications: a forwarding system, a cellular system blocking, slotted ALOHA, Wi-Fi model, and multichannel based LAN model. The examples cover CTMC, DTMC, birth-death process and non birth-death process. We then introduce more difficult examples in Chapter 4, which are related to wireless LAN networks: the Bianchi model and Multi-Channel MAC model with fixed duration. These models are more advanced than those introduced in Chapter 3 because they require more advanced concepts such as renewal-reward theorem and the queueing network model. We introduce these concepts in the appendix as needed so that readers can follow them without difficulty. We hope that this textbook will be helpful to students, researchers, and network practitioners who want to understand and use mathematical modeling techniques. Table of Contents: Performance Modeling / Markov Chain Modeling / Developing Markov Chain Performance Models / Advanced Markov Chain Models
Markov Chains
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Author : Wai-Ki Ching
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-27
Markov Chains written by Wai-Ki Ching 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 2013-03-27 with Business & Economics categories.
This new edition of Markov Chains: Models, Algorithms and Applications has been completely reformatted as a text, complete with end-of-chapter exercises, a new focus on management science, new applications of the models, and new examples with applications in financial risk management and modeling of financial data. This book consists of eight chapters. Chapter 1 gives a brief introduction to the classical theory on both discrete and continuous time Markov chains. The relationship between Markov chains of finite states and matrix theory will also be highlighted. Some classical iterative methods for solving linear systems will be introduced for finding the stationary distribution of a Markov chain. The chapter then covers the basic theories and algorithms for hidden Markov models (HMMs) and Markov decision processes (MDPs). Chapter 2 discusses the applications of continuous time Markov chains to model queueing systems and discrete time Markov chain for computing the PageRank, the ranking of websites on the Internet. Chapter 3 studies Markovian models for manufacturing and re-manufacturing systems and presents closed form solutions and fast numerical algorithms for solving the captured systems. In Chapter 4, the authors present a simple hidden Markov model (HMM) with fast numerical algorithms for estimating the model parameters. An application of the HMM for customer classification is also presented. Chapter 5 discusses Markov decision processes for customer lifetime values. Customer Lifetime Values (CLV) is an important concept and quantity in marketing management. The authors present an approach based on Markov decision processes for the calculation of CLV using real data. Chapter 6 considers higher-order Markov chain models, particularly a class of parsimonious higher-order Markov chain models. Efficient estimation methods for model parameters based on linear programming are presented. Contemporary research results on applications to demand predictions, inventory control and financial risk measurement are also presented. In Chapter 7, a class of parsimonious multivariate Markov models is introduced. Again, efficient estimation methods based on linear programming are presented. Applications to demand predictions, inventory control policy and modeling credit ratings data are discussed. Finally, Chapter 8 re-visits hidden Markov models, and the authors present a new class of hidden Markov models with efficient algorithms for estimating the model parameters. Applications to modeling interest rates, credit ratings and default data are discussed. This book is aimed at senior undergraduate students, postgraduate students, professionals, practitioners, and researchers in applied mathematics, computational science, operational research, management science and finance, who are interested in the formulation and computation of queueing networks, Markov chain models and related topics. Readers are expected to have some basic knowledge of probability theory, Markov processes and matrix theory.