Stochastic Ordering and Dependence in Applied Probability

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. Language: English