Author | Szekli, R. author |
---|---|
Title | Stochastic Ordering and Dependence in Applied Probability [electronic resource] / by R. Szekli |
Imprint | New York, NY : Springer New York, 1995 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2528-7 |
Descript | VIII, 194 p. online resource |
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 Strassenโs 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