Applied Stochastic System Modeling
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Applied Stochastic System Modeling
Author: Shunji Osaki
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
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.
Applied Stochastic Modelling
Highlighting modern computational methods, Applied Stochastic Modelling, Second Edition provides students with the practical experience of scientific computing in applied statistics through a range of interesting real-world applications. It also successfully revises standard probability and statistical theory. Along with an updated bibliography and
Stochastic Modeling and Optimization
Author: David D. Yao
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
The objective of this volume is to highlight through a collection of chap ters some of the recent research works in applied prob ability, specifically stochastic modeling and optimization. The volume is organized loosely into four parts. The first part is a col lection of several basic methodologies: singularly perturbed Markov chains (Chapter 1), and related applications in stochastic optimal control (Chapter 2); stochastic approximation, emphasizing convergence properties (Chapter 3); a performance-potential based approach to Markov decision program ming (Chapter 4); and interior-point techniques (homogeneous self-dual embedding and central path following) applied to stochastic programming (Chapter 5). The three chapters in the second part are concerned with queueing the ory. Chapters 6 and 7 both study processing networks - a general dass of queueing networks - focusing, respectively, on limit theorems in the form of strong approximation, and the issue of stability via connections to re lated fluid models. The subject of Chapter 8 is performance asymptotics via large deviations theory, when the input process to a queueing system exhibits long-range dependence, modeled as fractional Brownian motion.