Applied Stochastic System Modeling

by Shunji Osaki

This book provides a self-contained and systematic treatment of stochastic processes and their applications. Having a ba- sic knowledge of mathematics at an undergraduate level, the reader can easily understand stochastic processes with dis- crete state space such as Poisson processes, renewal proces- ses and Markov chains. Fruitful applications of such proces- sesare also described in the real world problems in relia- bility 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

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Year of publication:	1992
Authors:	Osaki, Shunji
Publisher:	Berlin, Heidelberg : Springer Berlin Heidelberg
Subject:	Stochastischer Prozess \| Stochastic process \| Theorie \| Theory \| Wahrscheinlichkeitsrechnung \| Probability theory \| Operations Research \| Operations research

Extent:	Online-Ressource (IX, 269p. 55 illus) online resource
Type of publication:	Book / Working Paper
Language:	English
Notes:	1 Probability Theory1.1 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 -- 8.5 Ordering Models -- 8.6 Problems 8 -- 9 Queueing Models -- 9.1 Introduction -- 9.2 Single Server Queueing Models -- 9.3 Multiple Server Queueing Models -- 9.4 Queues with a Finite Population -- 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.
ISBN:	978-3-642-84681-6 ; 978-3-642-84683-0
Other identifiers:	10.1007/978-3-642-84681-6 [DOI]
Source:	ECONIS - Online Catalogue of the ZBW

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