Modeling and Analysis of Stochastic Systems

ISBN-13: 9780367736798 / Angielski / Miękka / 2020 / 584 str.

Vidyadhar G. Kulkarni

Opis

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

Recenzje

"The third edition of Modeling and Analysis of Stochastic Systems remains an excellent book for a graduate-level study of stochastic processes. The aim of the book is modeling with stochastic elements in practical settings and analysis of the resulting stochastic model. The target audience is quantitative disciplines such as operations research, statistics, computer science, economics, and others where the book is well positioned, since it is application-driven and does not require measure theoretic probability. … The numerous exercises, separated into modeling, computational, and conceptual classes, are a strength of this text. The author also notes that most come from his own homework and exams, making them a valuable resource."
—James M. Flegal, University of California, Riverside, in Journal of the American Statistical Association, January 2018

Spis treści

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 ExercisesDiscrete-Time Markov Chains: First Passage TimesDefinitionsCumulative Distribution Function of TAbsorption ProbabilitiesExpectation of TGenerating Function and Higher Moments of TComputational ExercisesConceptual ExercisesDiscrete-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 ExercisesPoisson ProcessesExponential DistributionsPoisson Process: DefinitionsEvent Times in a Poisson ProcessSuperposition and Splitting of Poisson ProcessesNon-Homogeneous Poisson ProcessCompound Poisson ProcessComputational ExercisesConceptual ExercisesContinuous-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 Irre

O autorze

Vidyadhar G. Kulkarni