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Scholastic Ordering and Dependence in Applied Probability : Lecture Notes in Statistics - R. Szekli

Scholastic Ordering and Dependence in Applied Probability

Lecture Notes in Statistics

By: R. Szekli

Paperback ISBN: 9780387944500
Number Of Pages: 194

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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.

Univariate Orderingp. 1
Construction of iid random variablesp. 2
Strong orderingp. 6
Convex orderingp. 10
Conditional orderingsp. 19
Relative inverse function orderingsp. 22
Dispersive orderingp. 29
Compoundingp. 31
Integral orderings for queuesp. 34
Relative inverse orderings for queuesp. 40
Loss systemsp. 42
Multivariate Orderingp. 47
Strassen's theoremp. 47
Coupling constructionsp. 51
Conditioningp. 60
Markov processesp. 64
Point processes on R, martingalesp. 73
Markovian queues and Jackson networksp. 83
Poissonian flows and product formulap. 88
Stochastic ordering of Markov processesp. 92
Stochastic ordering of point processesp. 98
Renewal processesp. 104
Comparison of replacement policiesp. 109
Stochastically monotone networksp. 117
Queues with MR arrivalsp. 125
Dependencep. 135
Associationp. 136
MTP[subscript 2]p. 139
A general theory of positive dependencep. 143
Multivariate orderings and dependencep. 145
Negative associationp. 148
Independence via uncorrelatednessp. 152
Association for Markov processesp. 155
Dependencies in Markovian networksp. 159
Dependencies in Markov renewal queuesp. 164
Associated point processesp. 169
A.1 Probability spacesp. 173
A.2 Distribution functionsp. 175
A.3 Examples of distribution functionsp. 178
A.4 Other characteristics of probability measuresp. 180
A.5 Random variables equal in distributionp. 182
A.6 Bibliographyp. 184
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387944500
ISBN-10: 0387944508
Series: Lecture Notes in Statistics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 194
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.39 x 15.6  x 1.14
Weight (kg): 0.3

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