Overview

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.

Full Product Details

Author:   Shunji Osaki
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Weight:   0.570kg
ISBN:  

9783540549277

ISBN 10:   3540549277
Pages:   269
Publication Date:   17 January 1992
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

1 Probability Theory.- 1.1 Introduction.- 1.2 Sample Spaces and Events.- 1.3 Probabilities.- 1.4 Combinatorial Analysis.- 1.5 Problems 1.- 2 Random Variables and Distributions.- 2.1 Introduction.- 2.2 Random Variables and Distributions.- 2.3 Discrete Distributions.- 2.4 Continuous Distributions.- 2.5 Multivariate Distributions.- 2.6 Limit Theorems.- 2.7 Problems 2.- 3 Poisson Processes.- 3.1 Stochastic Processes.- 3.2 The Poisson Process.- 3.3 Interarrival Time Distributions.- 3.4 Conditional Waiting Time Distributions.- 3.5 Nonhomogeneous Poisson Processes.- 3.6 Problems 3.- 4 Renewal Processes.- 4.1 Introduction.- 4.2 Renewal Functions.- 4.3 Limit Theorems.- 4.4 Delayed and Stationary Renewal Processes.- 4.5 Problems 4.- 5 Discrete-Time Markov Chains.- 5.1 Introduction.- 5.2 Chapman-Kolmogorov Equation.- 5.3 State Classification.- 5.4 Limiting Probabilities.- 5.5 Finite-State Markov Chains.- 5.6 Problems 5.- 6 Continuous-Time Markov Chains.- 6.1 Introduction.- 6.2 Pure Birth Processes.- 6.3 Pure Death Processes.- 6.4 Birth and Death Processes.- 6.5 Finite-State Markov Chains.- 6.6 Problems 6.- 7 Markov Renewal Processes.- 7.1 Introduction.- 7.2 Markov Renewal Processes.- 7.3 Stationary Probabilities.- 7.4 Alternating Renewal Processes.- 7.5 Problems 7.- 8 Reliability Models.- 8.1 Introduction.- 8.2 Lifetime Distributions and Failure Rates.- 8.3 Availability Theory.- 8.4 Replacement Models.- 8.4.1 Age Replacement Models.- 8.4.2 Block Replacement Models.- 8.5 Ordering Models.- 8.5.1 Model I.- 8.5.2 Model II.- 8.6 Problems 8.- 9 Queueing Models.- 9.1 Introduction.- 9.2 Single Server Queueing Models.- 9.2.1 M/M/1/? Queueing Models.- 9.2.2 M/M/1/N Queueing Models.- 9.3 Multiple Server Queueing Models.- 9.3.1 M/M/c/?Queueing Models.- 9.3.2 M/M/c/c Queueing Models.- 9.3.3 M/M/?/? Queueing Models.- 9.4 Queues with a Finite Population.- 9.4.1 M/M/1/K/K Queueing Models.- 9.4.2 M/M/c/K/K Queueing Models.- 9.4.3 M/M/c/c/c Queueing Models.- 9.5 Problems 9.- A Laplace-Stieltjes Transforms.- A.1 Laplace-Stieltjes Transforms.- A.2 Properties of Laplace-Stieltjes Transforms.- A.3 Applications to Distributions.- A.4 Applications to Differential Equations.- A.5 Applications to Renewal Functions.- B Answers to Selected Problems.- C The Bibliography.

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