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Modeling and Analysis of Stochastic Systems, Third Edition.

Author: Vidyadhar G Kulkarni
Publisher: Boca Raton : CRC Press, 2016.
Series: Chapman & Hall/CRC Texts in Statistical Science.
Edition/Format:   eBook : Document : English : 3rd ed
Database:WorldCat
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Kulkarni, Vidyadhar G.
Modeling and Analysis of Stochastic Systems, Third Edition.
Boca Raton : CRC Press, ©2016
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Vidyadhar G Kulkarni
ISBN: 9781498756624 149875662X
OCLC Number: 964408677
Notes: 6.3.5 Dealership Markets.
Description: 1 online resource (606 pages).
Contents: Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Preface; 1: Introduction; 1.1 What in the World Is a Stochastic Process?; 1.2 How to Characterize a Stochastic Process; 1.3 What Do We Do with a Stochastic Process?; 1.3.1 Characterization; 1.3.2 Transient Behavior; 1.3.3 First Passage Times; 1.3.4 Limiting Distribution; 1.3.5 Costs and Rewards; 2: Discrete-TimeMarkov Chains: Transient Behavior; 2.1 Definition and Characterization; 2.2 Examples; 2.3 DTMCs in Other Fields; 2.3.1 Genomics; 2.3.2 Genetics; 2.3.3 Genealogy; 2.3.4 Finance; 2.3.5 Manpower Planning. 2.3.6 Telecommunications2.3.7 Google Search; 2.4 Marginal Distributions; 2.5 Occupancy Times; 2.6 Computation of Matrix Powers; 2.6.1 Method of Diagonalization; 2.6.2 Method of Generating Functions; 2.7 Modeling Exercises; 2.8 Computational Exercises; 2.9 Conceptual Exercises; 3: Discrete-TimeMarkov Chains: First Passage Times; 3.1 Definitions; 3.2 Cumulative Distribution Function of T; 3.3 Absorption Probabilities; 3.4 Expectation of T; 3.5 Generating Function and Higher Moments of T; 3.6 Computational Exercises; 3.7 Conceptual Exercises; 4: Discrete-TimeMarkov Chains: Limiting Behavior. 4.1 Exploring the Limiting Behavior by Examples4.2 Classification of States; 4.2.1 Irreducibility; 4.2.2 Recurrence and Transience; 4.2.3 Periodicity; 4.3 Determining Recurrence and Transience: Finite DTMCs; 4.4 Determining Recurrence and Transience: Infinite DTMCs; 4.4.1 Foster's Criterion; 4.5 Limiting Behavior of Irreducible DTMCs; 4.5.1 The Transient Case; 4.5.2 The Discrete Renewal Theorem; 4.5.3 The Recurrent Case; 4.5.4 The Null Recurrent Case; 4.5.5 The Positive Recurrent Aperiodic Case; 4.5.6 The Positive Recurrent Periodic Case. 4.5.7 Necessary and Sufficient Condition for Positive Recurrence4.5.8 Examples; 4.6 Examples: Limiting Behavior of Infinite State-Space Irreducible DTMCs; 4.7 Limiting Behavior of Reducible DTMCs; 4.8 DTMCs with Costs and Rewards; 4.8.1 Discounted Costs; 4.8.2 Average Costs; 4.9 Reversibility; 4.10 Computational Exercises; 4.11 Conceptual Exercises; 5: Poisson Processes; 5.1 Exponential Distributions; 5.1.1 Memoryless Property; 5.1.2 Hazard Rate; 5.1.3 Probability of First Failure; 5.1.4 Minimum of Exponentials; 5.1.5 Strong Memoryless Property; 5.1.6 Sum of iid Exponentials. 5.1.7 Sum of Distinct Exponentials5.1.8 Random Sums of iid Exponentials; 5.2 Poisson Process: Definitions; 5.3 Event Times in a Poisson Process; 5.4 Superposition and Splitting of Poisson Processes; 5.4.1 Superposition; 5.4.2 Splitting; 5.5 Non-Homogeneous Poisson Process; 5.5.1 Event Times in an NPP; 5.6 Compound Poisson Process; 5.7 Computational Exercises; 5.8 Conceptual Exercises; 6: Continuous-Time Markov Chains; 6.1 Definitions and Sample Path Properties; 6.2 Examples; 6.3 CTMCs in Other Fields; 6.3.1 Organ Transplants; 6.3.2 Disease Progression; 6.3.3 Epidemics; 6.3.4 Order Books.
Series Title: Chapman & Hall/CRC Texts in Statistical Science.

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