Applied Stochastic System Modelling - Hardcover

Osaki, Shunji

Hardcover

ISBN 10: 3540549277 ISBN 13: 9783540549277

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1992

Synopsis

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.

About this title

Synopsis

This book provides a self-contained and systematic treatment of stochastic processes and their applications. Having a basic knowledge of mathematics at an undergraduate level, the reader should be able to understand stochastic processes with discrete state space such as Poisson processes renewal processes and Markov chains. Fruitful applications of such processes are also described in the real world problems in reliability and queueing models. Numerous illustrations are included for better understanding. Problems are included in each chapter. Appendices are devoted to the Laplace-Stieltjes transforms and their properties, and answers to selected problems. It is suitable for an introductory one-semester or two-quarter course in stochastic processes for the junior or senior undergraduate students.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1992
• Language: English
• ISBN 10: 3540549277
• ISBN 13: 9783540549277
• Binding: Hardcover
• Number of pages: 269