Kulkarni Modeling and Analysis of Stochastic Systems

3. Auflage 2016
ISBN: 978-1-4987-5672-3
Verlag: CRC Press
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 606 Seiten

Reihe: Chapman & Hall/CRC Texts in Statistical Science

Building on the author’s more than 35 years of teaching experience, Modeling and Analysis of Stochastic Systems, Third Edition, covers the most important classes of stochastic processes used in the modeling of diverse systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models.

The third edition has been updated with several new applications, including the Google search algorithm in discrete time Markov chains, several examples from health care and finance in continuous time Markov chains, and square root staffing rule in Queuing models. More than 50 new exercises have been added to enhance its use as a course text or for self-study. The sequence of chapters and exercises has been maintained between editions, to enable those now teaching from the second edition to use the third edition.
Rather than offer special tricks that work in specific problems, this book provides thorough coverage of general tools that enable the solution and analysis of stochastic models. After mastering the material in the text, readers will be well-equipped to build and analyze useful stochastic models for real-life situations.

Autoren/Hrsg.

Kulkarni, Vidyadhar G.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik
• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensforschung

Inhaltsverzeichnis

IntroductionWhat in the World is a Stochastic Process?How to Characterize a Stochastic ProcessWhat Do We Do with a Stochastic Process?
Discrete-Time Markov Chains: Transient BehaviourDefinition and CharacterizationExamplesDTMCs in Other FieldsMarginal DistributionsOccupancy TimesComputation of Matrix PowersModeling ExercisesComputational ExercisesConceptual Exercises
Discrete-Time Markov Chains: First Passage TimesDefinitionsCumulative Distribution Function of TAbsorption ProbabilitiesExpectation of TGenerating Function and Higher Moments of TComputational ExercisesConceptual Exercises
Discrete-Time Markox Chains: Limiting BehaviourExploring the Limiting Behaviour by ExamplesClassification of StatesDetermining Recurrence and Transience: Finite DTMCsDetermining Recurrence and Transience: Infinite DTMScLimiting Behaviour of Irreducible DTMCsExamples: Limiting Behaviour of Infinite State-Space Irreducible DTMCsLimiting Behaviour of Reducible DTMCsDTMCs with Costs and RewardsReversibilityComputational ExercisesConceptual Exercises
Poisson ProcessesExponential DistributionsPoisson Process: DefinitionsEvent Times in a Poisson ProcessSuperposition and Splitting of Poisson ProcessesNon-Homogeneous Poisson ProcessCompound Poisson ProcessComputational ExercisesConceptual Exercises
Continuous-Time Markov ChainsDefinitions and Sample Path PropertiesExamplesCTMCs in Other FieldsTransient Behaviour: Marginal DistributionTransient Behaviour: Occupancy TimesComputation of P(t): Finite State-SpaceComputation of P(t): Infinite State-SpaceFirst-Passage TimesExploring the Limiting Behaviour by ExamplesClassification of StatesLimiting Behaviour of Irreducible CTMCsLimiting Behaviour of Reducible CTMCsCTMCs with Costs and RewardsPhase Type Distributions ReversibilityModeling ExercisesComputational ExercisesConceptual Exercises
Queueing ModelsIntroductionProperties of General Queueing SystemsBirth and Death QueuesOpen Queueing NetworksClosed Queueing NetworksSingle Server QueuesRetrial QueueInfinite Server QueueModeling ExercisesComputational Exercises
Renewal ProcessesIntroductionProperties of N(t)The Renewal FunctionRenewal-Type EquationKey Renewal TheoremRecurrence TimesDelayed Renewal ProcessesSemi-Markov ProcessesRenewal Processes with Costs/RewardsRegenerative ProcessesComputational ExercisesConceptual Exercises
Markov Regenerative ProcessesDefinitions and ExamplesMarkov Renewal Process and Markov Renewal FunctionKey Renewal Theorem for MRPs Semi-Markov Processes: Further ResultsMarkov Regenerative ProcessesApplications to QueuesModeling ExercisesComputational ExercisesConceptual Exercises
Diffusion ProcessBrownian MotionSample Path Properties of BMKolmogorov Equations for Standard Brownian MotionFirst Passage TimesReflected SBMReflected BM and Limiting DistributionsBM and MartingalesCost/Reward ModelsStochastic IntegrationStochastic Differential Equations and Ito's FormulaApplications to FinanceComputational ExercisesConceptual Exercises
Epilogue
Probability of Events
AppendicesUnivariate Random VariablesMultivariate Random VariablesGenerating FunctionsLaplace-Stieltjes TransformsLaplace TransformsModes of ConvergenceResults from AnalysisDifference and Differential Equations
Answers to Selected Problems
References
Index

Über Autor(innen)

Vidyadhar G. Kulkarni