Stochastic Ordering and Dependence in Applied Probability
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Stochastic Ordering and Dependence in Applied Probability: Enhancing Ethical Analyses of Reprogenetic Technologies(97 Lecture Notes in Statistics)

Stochastic Ordering and Dependence in Applied Probability: Enhancing Ethical Analyses of Reprogenetic Technologies(97 Lecture Notes in Statistics)

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About the Book

This is an introductory course in stochastic orderings and dependence, and their applications to queues and networks of queues. Readers are assumed to have a firm grounding in Lebesgue measure, conditional expectation, and martingales. Chapter 1 presents a collection of one-dimensional orderings with applications to the theory of queues. Chapter 2 extends these concepts to stochastic orderings in many dimensional spaces and functional spaces. Then results are given on stochastic ordering of networks, replacement policies, and single-server queues associated with Markov renewal processes. Finally, Chapter 3 is devoted to dependence and the relations between dependence and orderings. It includes applications to queueing networks and point processes.

Table of Contents:
1 Univariate Ordering.- 1.1 Construction of iid random variables.- 1.2 Strong ordering.- 1.3 Convex ordering.- 1.4 Conditional orderings.- 1.5 Relative inverse function orderings.- 1.6 Dispersive ordering.- 1.7 Compounding.- 1.8 Integral orderings for queues.- 1.9 Relative inverse orderings for queues.- 1.10 Loss systems.- 2 Multivariate Ordering.- 2.1 Strassen’s theorem.- 2.2 Coupling constructions.- 2.3 Conditioning.- 2.4 Markov processes.- 2.5 Point processes on R, martingales.- 2.6 Markovian queues and Jackson networks.- 2.7 Poissonian flows and product formula.- 2.8 Stochastic ordering of Markov processes.- 2.9 Stochastic ordering of point processes.- 2.10 Renewal processes.- 2.11 Comparison of replacement policies.- 2.12 Stochastically monotone networks.- 2.13 Queues with MR arrivals.- 3 Dependence.- 3.1 Association.- 3.2 MTP2.- 3.3 A general theory of positive dependence.- 3.4 Multivariate orderings and dependence.- 3.5 Negative association.- 3.6 Independence via uncorrelatedness.- 3.7 Association for Markov processes.- 3.8 Dependencies in Markovian networks.- 3.9 Dependencies in Markov renewal queues.- 3.10 Associated point processes.- A.- A.1 Probability spaces.- A.2 Distribution functions.- A.3 Examples of distribution functions.- A.4 Other characteristics of probability measures.- A.5 Random variables equal in distribution.- A.6 Bibliography.


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Product Details
  • ISBN-13: 9780387944500
  • Publisher: Springer-Verlag New York Inc.
  • Publisher Imprint: Springer-Verlag New York Inc.
  • Height: 235 mm
  • No of Pages: 194
  • Returnable: N
  • Spine Width: 33 mm
  • Weight: 354 gr
  • ISBN-10: 0387944508
  • Publisher Date: 24 Jan 1995
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Series Title: 97 Lecture Notes in Statistics
  • Sub Title: Enhancing Ethical Analyses of Reprogenetic Technologies
  • Width: 155 mm


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