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- catalog abstract "This book presents 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, and it includes applications to queueing networks and point processes.".
- catalog contributor b7548929.
- catalog created "c1995.".
- catalog date "1995".
- catalog date "c1995.".
- catalog dateCopyrighted "c1995.".
- catalog description "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. MTP[subscript 2]. 3.3. A general theory of positive dependence. 3.4. Multivariate orderings and dependence. 3.5. Negative association.".
- catalog description "Includes bibliographical references and index.".
- catalog description "This book presents 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, and it includes applications to queueing networks and point processes.".
- catalog extent "viii, 194 p. ;".
- catalog hasFormat "Stochastic ordering and dependence in applied probability.".
- catalog identifier "0387944508 (acid-free)".
- catalog isFormatOf "Stochastic ordering and dependence in applied probability.".
- catalog isPartOf "Lecture notes in statistics (Springer-Verlag) ; v. 97.".
- catalog isPartOf "Lecture notes in statistics ; 97".
- catalog issued "1995".
- catalog issued "c1995.".
- catalog language "eng".
- catalog publisher "New York : Springer-Verlag,".
- catalog relation "Stochastic ordering and dependence in applied probability.".
- catalog subject "519.2 20".
- catalog subject "Distribution (Probability theory).".
- catalog subject "Mathematics.".
- catalog subject "Probabilities.".
- catalog subject "QA273 .S93 1995".
- catalog subject "Stochastic processes.".
- catalog tableOfContents "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. MTP[subscript 2]. 3.3. A general theory of positive dependence. 3.4. Multivariate orderings and dependence. 3.5. Negative association.".
- catalog title "Stochastic ordering and dependence in applied probability / R. Szekli.".
- catalog type "text".