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## Markov Processes for Stochastic Modeling

- Author : Oliver Ibe
- Publisher :Unknown
- Release Date :2013-05-22
- Total pages :514
- ISBN : 9780124078390

**Summary :** Markov processes are processes that have limited memory. In particular, their dependence on the past is only through the previous state. They are used to model the behavior of many systems including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. Covering a wide range of areas of application of Markov processes, this second edition is revised to highlight the most important aspects as well as the most recent trends and applications of Markov processes. The author spent over 16 years in the industry before returning to academia, and he has applied many of the principles covered in this book in multiple research projects. Therefore, this is an applications-oriented book that also includes enough theory to provide a solid ground in the subject for the reader. Presents both the theory and applications of the different aspects of Markov processes Includes numerous solved examples as well as detailed diagrams that make it easier to understand the principle being presented Discusses different applications of hidden Markov models, such as DNA sequence analysis and speech analysis.

## Markov Processes for Stochastic Modeling

- Author : Oliver Ibe
- Publisher :Unknown
- Release Date :2008-09-02
- Total pages :512
- ISBN : 9780080922454

**Summary :** Markov processes are used to model systems with limited memory. They are used in many areas including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. This book, which is written for upper level undergraduate and graduate students, and researchers, presents a unified presentation of Markov processes. In addition to traditional topics such as Markovian queueing system, the book discusses such topics as continuous-time random walk,correlated random walk, Brownian motion, diffusion processes, hidden Markov models, Markov random fields, Markov point processes and Markov chain Monte Carlo. Continuous-time random walk is currently used in econophysics to model the financial market, which has traditionally been modelled as a Brownian motion. Correlated random walk is popularly used in ecological studies to model animal and insect movement. Hidden Markov models are used in speech analysis and DNA sequence analysis while Markov random fields and Markov point processes are used in image analysis. Thus, the book is designed to have a very broad appeal. - Provides the practical, current applications of Markov processes - Coverage of HMM, Point processes, and Monte Carlo - Includes enough theory to help students gain throrough understanding of the subject - Principles can be immediately applied in many specific research projects, saving researchers time - End of chapter exercises provide reinforcement, practice and increased understanding to the student

## Student Solutions Manual for Markov Processes for Stochastic Modeling

- Author : Oliver Ibe
- Publisher :Unknown
- Release Date :2008-11-21
- Total pages :120
- ISBN : 9780080952147

**Summary :** Student Solutions Manual for Markov Processes for Stochastic Modeling

## From Application to Theory: Markov Processes in Stochastic Modeling of Transport Phenomena

- Author : Timo Gottschalk
- Publisher :Unknown
- Release Date :2007
- Total pages :229
- ISBN : OCLC:1184302960

**Summary :**

## Markov Processes for Stochastic Modeling

- Author : Masaaki Kijima
- Publisher :Unknown
- Release Date :2013-12-19
- Total pages :341
- ISBN : 9781489931320

**Summary :** This book presents an algebraic development of the theory of countable state space Markov chains with discrete- and continuous-time parameters. A Markov chain is a stochastic process characterized by the Markov prop erty that the distribution of future depends only on the current state, not on the whole history. Despite its simple form of dependency, the Markov property has enabled us to develop a rich system of concepts and theorems and to derive many results that are useful in applications. In fact, the areas that can be modeled, with varying degrees of success, by Markov chains are vast and are still expanding. The aim of this book is a discussion of the time-dependent behavior, called the transient behavior, of Markov chains. From the practical point of view, when modeling a stochastic system by a Markov chain, there are many instances in which time-limiting results such as stationary distributions have no meaning. Or, even when the stationary distribution is of some importance, it is often dangerous to use the stationary result alone without knowing the transient behavior of the Markov chain. Not many books have paid much attention to this topic, despite its obvious importance.

## An Introduction to Stochastic Modeling

- Author : Howard M. Taylor,Samuel Karlin
- Publisher :Unknown
- Release Date :2014-05-10
- Total pages :410
- ISBN : 9781483269276

**Summary :** An Introduction to Stochastic Modeling 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.

## Stochastic Modeling

- Author : Barry L. Nelson
- Publisher :Unknown
- Release Date :2012-10-11
- Total pages :336
- ISBN : 9780486139944

**Summary :** Coherent introduction to techniques also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Includes formulation of models, analysis, and interpretation of results. 1995 edition.

## Stochastic Modeling of Scientific Data

- Author : Peter Guttorp,Vladimir N. Minin
- Publisher :Unknown
- Release Date :2018-03-29
- Total pages :384
- ISBN : 9781351413657

**Summary :** Stochastic Modeling of Scientific Data combines stochastic modeling and statistical inference in a variety of standard and less common models, such as point processes, Markov random fields and hidden Markov models in a clear, thoughtful and succinct manner. The distinguishing feature of this work is that, in addition to probability theory, it contains statistical aspects of model fitting and a variety of data sets that are either analyzed in the text or used as exercises. Markov chain Monte Carlo methods are introduced for evaluating likelihoods in complicated models and the forward backward algorithm for analyzing hidden Markov models is presented. The strength of this text lies in the use of informal language that makes the topic more accessible to non-mathematicians. The combinations of hard science topics with stochastic processes and their statistical inference puts it in a new category of probability textbooks. The numerous examples and exercises are drawn from astronomy, geology, genetics, hydrology, neurophysiology and physics.

## Probability and Stochastic Modeling

- Author : Vladimir I. Rotar
- Publisher :Unknown
- Release Date :2012-08-25
- Total pages :508
- ISBN : 9781439872062

**Summary :** A First Course in Probability with an Emphasis on Stochastic Modeling Probability and Stochastic Modeling not only covers all the topics found in a traditional introductory probability course, but also emphasizes stochastic modeling, including Markov chains, birth-death processes, and reliability models. Unlike most undergraduate-level probability texts, the book also focuses on increasingly important areas, such as martingales, classification of dependency structures, and risk evaluation. Numerous examples, exercises, and models using real-world data demonstrate the practical possibilities and restrictions of different approaches and help students grasp general concepts and theoretical results. The text is suitable for majors in mathematics and statistics as well as majors in computer science, economics, finance, and physics. The author offers two explicit options to teaching the material, which is reflected in "routes" designated by special "roadside" markers. The first route contains basic, self-contained material for a one-semester course. The second provides a more complete exposition for a two-semester course or self-study.

## Cycle Representations of Markov Processes

- Author : Sophia L. Kalpazidou
- Publisher :Unknown
- Release Date :2013-06-29
- Total pages :194
- ISBN : 9781475739299

**Summary :** This book provides new insight into Markovian dependence via the cycle decompositions. It presents a systematic account of a class of stochastic processes known as cycle (or circuit) processes - so-called because they may be defined by directed cycles. An important application of this approach is the insight it provides to electrical networks and the duality principle of networks. This expanded second edition adds new advances, which reveal wide-ranging interpretations of cycle representations such as homologic decompositions, orthogonality equations, Fourier series, semigroup equations, and disintegration of measures. The text includes chapter summaries as well as a number of detailed illustrations.

## Elements of Stochastic Modelling

- Author : Konstantin Borovkov
- Publisher :Unknown
- Release Date :2014-06-30
- Total pages :500
- ISBN : 9789814571180

**Summary :** This is the expanded second edition of a successful textbook that provides a broad introduction to important areas of stochastic modelling. The original text was developed from lecture notes for a one-semester course for third-year science and actuarial students at the University of Melbourne. It reviewed the basics of probability theory and then covered the following topics: Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation. The present edition adds new chapters on elements of stochastic calculus and introductory mathematical finance that logically complement the topics chosen for the first edition. This makes the book suitable for a larger variety of university courses presenting the fundamentals of modern stochastic modelling. Instead of rigorous proofs we often give only sketches of the arguments, with indications as to why a particular result holds and also how it is related to other results, and illustrate them by examples. Wherever possible, the book includes references to more specialised texts on respective topics that contain both proofs and more advanced material. Request Inspection Copy

## Stochastic Modelling of Social Processes

- Author : Andreas Diekmann,Peter Mitter
- Publisher :Unknown
- Release Date :2014-05-10
- Total pages :352
- ISBN : 9781483266565

**Summary :** Stochastic Modelling of Social Processes provides information pertinent to the development in the field of stochastic modeling and its applications in the social sciences. This book demonstrates that stochastic models can fulfill the goals of explanation and prediction. Organized into nine chapters, this book begins with an overview of stochastic models that fulfill normative, predictive, and structural–analytic roles with the aid of the theory of probability. This text then examines the study of labor market structures using analysis of job and career mobility, which is one of the approaches taken by sociologists in research on the labor market. Other chapters consider the characteristic trends and patterns from data on divorces. This book discusses as well the two approaches of stochastic modeling of social processes, namely competing risk models and semi-Markov processes. The final chapter deals with the practical application of regression models of survival data. This book is a valuable resource for social scientists and statisticians.

## Elements of Stochastic Modelling

- Author : K. A. Borovkov
- Publisher :Unknown
- Release Date :2003
- Total pages :342
- ISBN : 9812383018

**Summary :** This textbook has been developed from the lecture notes for a one-semester course on stochastic modelling. It reviews the basics of probability theory and then covers the following topics: Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation. Rigorous proofs are often replaced with sketches of arguments ? with indications as to why a particular result holds, and also how it is connected with other results ? and illustrated by examples. Wherever possible, the book includes references to more specialised texts containing both proofs and more advanced material related to the topics covered.

## An Introduction to Stochastic Modeling

- Author : Mark Pinsky,Samuel Karlin
- Publisher :Unknown
- Release Date :2011
- Total pages :563
- ISBN : 9780123814166

**Summary :** 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

## Stochastic Modeling and Analysis of Telecom Networks

- Author : Laurent Decreusefond,Pascal Moyal
- Publisher :Unknown
- Release Date :2012-12-27
- Total pages :387
- ISBN : 9781118563045

**Summary :** This book addresses the stochastic modeling of telecommunicationnetworks, introducing the main mathematical tools for that purpose,such as Markov processes, real and spatial point processes andstochastic recursions, and presenting a wide list of results onstability, performances and comparison of systems. The authors propose a comprehensive mathematical construction ofthe foundations of stochastic network theory: Markov chains,continuous time Markov chains are extensively studied using anoriginal martingale-based approach. A complete presentation ofstochastic recursions from an ergodic theoretical perspective isalso provided, as well as spatial point processes. Using these basic tools, stability criteria, performance measuresand comparison principles are obtained for a wide class of models,from the canonical M/M/1 and G/G/1 queues to more sophisticatedsystems, including the current “hot topics” of spatialradio networking, OFDMA and real-time networks. Contents 1. Introduction. Part 1: Discrete-time Modeling 2. Stochastic Recursive Sequences. 3. Markov Chains. 4. Stationary Queues. 5. The M/GI/1 Queue. Part 2: Continuous-time Modeling 6. Poisson Process. 7. Markov Process. 8. Systems with Delay. 9. Loss Systems. Part 3: Spatial Modeling 10. Spatial Point Processes.

## Applied Stochastic System Modeling

- Author : Shunji Osaki
- Publisher :Unknown
- Release Date :2012-12-06
- Total pages :269
- ISBN : 9783642846816

**Summary :** This book was written for an introductory one-semester or two-quarter course in stochastic processes and their applications. The reader is assumed to have a basic knowledge of analysis and linear algebra at an undergraduate level. Stochastic models are applied in many fields such as engineering systems, physics, biology, operations research, business, economics, psychology, and linguistics. Stochastic modeling is one of the promising kinds of modeling in applied probability theory. This book is intended to introduce basic stochastic processes: Poisson pro cesses, renewal processes, discrete-time Markov chains, continuous-time Markov chains, and Markov-renewal processes. These basic processes are introduced from the viewpoint of elementary mathematics without going into rigorous treatments. This book also introduces applied stochastic system modeling such as reliability and queueing modeling. Chapters 1 and 2 deal with probability theory, which is basic and prerequisite to the following chapters. Many important concepts of probabilities, random variables, and probability distributions are introduced. Chapter 3 develops the Poisson process, which is one of the basic and im portant stochastic processes. Chapter 4 presents the renewal process. Renewal theoretic arguments are then used to analyze applied stochastic models. Chapter 5 develops discrete-time Markov chains. Following Chapter 5, Chapter 6 deals with continuous-time Markov chains. Continuous-time Markov chains have im portant applications to queueing models as seen in Chapter 9. A one-semester course or two-quarter course consists of a brief review of Chapters 1 and 2, fol lowed in order by Chapters 3 through 6.

## Controlled Markov Processes and Viscosity Solutions

- Author : Wendell H. Fleming,Halil Mete Soner
- Publisher :Unknown
- Release Date :2006-02-04
- Total pages :429
- ISBN : 9780387310718

**Summary :** This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.

## Statistical Topics and Stochastic Models for Dependent Data with Applications

- Author : Vlad Stefan Barbu,Nicolas Vergne
- Publisher :Unknown
- Release Date :2020-11-03
- Total pages :288
- ISBN : 9781119779407

**Summary :** This book is a collective volume authored by leading scientists in the field of stochastic modelling, associated statistical topics and corresponding applications. The main classes of stochastic processes for dependent data investigated throughout this book are Markov, semi-Markov, autoregressive and piecewise deterministic Markov models. The material is divided into three parts corresponding to: (i) Markov and semi-Markov processes, (ii) autoregressive processes and (iii) techniques based on divergence measures and entropies. A special attention is payed to applications in reliability, survival analysis and related fields.

## Stochastic Modeling and Optimization

- Author : David D. Yao,Hanqin Zhang,Xun Yu Zhou
- Publisher :Unknown
- Release Date :2012-12-06
- Total pages :468
- ISBN : 9780387217574

**Summary :** This books covers the broad range of research in stochastic models and optimization. Applications presented include networks, financial engineering, production planning, and supply chain management. Each contribution is aimed at graduate students working in operations research, probability, and statistics.

## Stochastic Modelling for Systems Biology, Third Edition

- Author : Darren J. Wilkinson
- Publisher :Unknown
- Release Date :2018-12-07
- Total pages :384
- ISBN : 9781351000901

**Summary :** Since the first edition of Stochastic Modelling for Systems Biology, there have been many interesting developments in the use of "likelihood-free" methods of Bayesian inference for complex stochastic models. Having been thoroughly updated to reflect this, this third edition covers everything necessary for a good appreciation of stochastic kinetic modelling of biological networks in the systems biology context. New methods and applications are included in the book, and the use of R for practical illustration of the algorithms has been greatly extended. There is a brand new chapter on spatially extended systems, and the statistical inference chapter has also been extended with new methods, including approximate Bayesian computation (ABC). Stochastic Modelling for Systems Biology, Third Edition is now supplemented by an additional software library, written in Scala, described in a new appendix to the book. New in the Third Edition New chapter on spatially extended systems, covering the spatial Gillespie algorithm for reaction diffusion master equation models in 1- and 2-d, along with fast approximations based on the spatial chemical Langevin equation Significantly expanded chapter on inference for stochastic kinetic models from data, covering ABC, including ABC-SMC Updated R package, including code relating to all of the new material New R package for parsing SBML models into simulatable stochastic Petri net models New open-source software library, written in Scala, replicating most of the functionality of the R packages in a fast, compiled, strongly typed, functional language Keeping with the spirit of earlier editions, all of the new theory is presented in a very informal and intuitive manner, keeping the text as accessible as possible to the widest possible readership. An effective introduction to the area of stochastic modelling in computational systems biology, this new edition adds additional detail and computational methods that will provide a stronger foundation for the development of more advanced courses in stochastic biological modelling.

## Markov Chains and Stochastic Stability

- Author : Sean Meyn,Richard L. Tweedie
- Publisher :Unknown
- Release Date :2009-04-02
- Total pages :594
- ISBN : 9780521731829

**Summary :** New up-to-date edition of this influential classic on Markov chains in general state spaces. Proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background. New commentary by Sean Meyn, including updated references, reflects developments since 1996.