On the application of the theory of probability to two combinatorial problems involving permutations

Kapitel in diesem Buch

1. Frontmatter 1
2. Editorial Note 5
3. CONTENTS 7
4. L'académicien Octave Onicescu à 90 ans 11
5. Invited papers
6. Probabilistic aspects of Jordan algebras 15
7. Rates of convergence and expansions for rank tests: A review and some remarks on the nuisance parameter case 23
8. Asymptotically efficient estimator for the index of a stable distribution 33
9. Some gambling problems with nonintuitive solutions 41
10. Some results on unimodal distribution functions 51
11. Some implications of metric tightness on sub o-fields of a probability space 57
12. Some remarks on strong mixing conditions 65
13. Reduction methods for the vertex packing problem 73
14. On weak and strong approximations of the quantile process 81
15. Strong Markov property for a class of transition semigroups 97
16. Asymptotic results for the pseudo-prime sequence generated by Hawkins'random sieve: Twin primes and Riemann's hypothesis 109
17. Rôles des matrices en statistique et problèmes qu'elles posent 117
18. Subexponential distribution functions and their applications: A review 125
19. On the application of the theory of probability to two combinatorial problems involving permutations 137
20. Stochastic models of economic dynamics and equilibrium: Asymptotic behaviour of equilibrium paths 149
21. Critical branching processes with general phase space 159
22. A central limit theorem for certain stopped sums and some applications 165
23. On the structure of solutions of stochastic dynamic programs 173
24. Multiple test unbiasedness 183
25. On sequential urn problems 195
26. Probabilities related to the random bombardment of a square 199
27. The stable asymptotic structure of growing branching populations 205
28. Duality theorems and probability metrics 211
29. Distributions with known marginals arid duality of mathematical programming with application to PERT 221
30. Ansätze und Ergebnissé der optimalen Planung von Experimenten mit sowohl qualitativen als auch quantitativen Einflussfaktoren 237
31. On the memory of a Markov chain. A decision theoretical approach 249
32. Recent results on multi-stage selection procedures 259
33. Non-homogeneous Markov chains: Tail idempotents, tail sigma-fields and basis 269
34. The role of the breakpoint in schistosomiasis eradication 283
35. On randomized statistical procedures 295
36. Some stochastic equations for quasi-diffusion processes 307
37. Wiener-Hopf factorization of Markov semigroups— I. The countable state space case 315
38. On the asymptotic behavior of the Shapiro-Wilk test 325
39. Me and the anthropologist 333
40. Bayesian approach to the analysis of clinical studies 345
41. Issues arising in multiple comparisons among populations 353
42. Problems of estimation in continuous-discrete stochastic models 363
43. Ein statistisches Modell für Bonituren 375
44. Rates of convergence for the stability of maxima 385
45. Indistinguishability of particles and exchangeable random variables 393
46. Communications
47. I. PROBABILITY
48. On measurability of the inverse of a random mapping with random domain 399
49. Some properties of random operators and applications to existence theorems for random equations 403
50. Conditional expectation with respect to dependent σ-fields 409
51. Changes of time associated with non-homogeneous regular Markov processes 413
52. Quelques remarques sur les métriques probabilistes 419
53. Continuous semi-Markov processes and an extremal property of Markov processes 423
54. A new stochastic model of turbulence 431
55. On the random Riemann hypothesis 435
56. On nonlinear filtering of Poisson driven dynamical systems 451
57. Convolution inverses and branching random walk 459
58. On the ergodicity of the tensor product of two stochastic systems 467
59. Two remarks on the Skorohod representation 471
60. On convergence rates of the strong law for stationary mixing sequences 473
61. A characterization of product-measurability of Radon-Nikodym derivatives by separability 477
62. Biased estimates for the solution of an integral equation 481
63. On a family of metrics for the distribution functions 487
64. Application of the orthonormal expansion of random functions to turbulent diffusion 493
65. On infinite dimensional continuous square integrable martingales with differentiable characteristics 497
66. An integral for decomposable measures and applications 507
67. Two inequalities concerning centered moments 515
68. II. Mathematical Statistics
69. Unbalancedness and efficiency in estimating components of variance 519
70. Estimate of P ( Y < X ) in case of the double exponential distribution 527
71. Quelques considérations statistiques concernant la loi normale généralisée 533
72. Tests of hypotheses based on maximal contrasts 537
73. On random number generation procedures 541
74. Matrix free computation of C. R. Rao's MINQUE and its sample variance under unbalanced nested classification models 547
75. Sur une extension de la méthode T de comparaison multiple 555
76. A generalized geometric distribution and some of its properties 559
77. General criteria for positive dependence 565
78. The generalized gamma distribution and the principle of maximum entropy 569
79. Numerical simulation of turbulent diffusion for a one-dimensional model 573
80. Multiplicative infinite divisibility of standard normal and gamma distributions 579
81. Multiple comparison techniques for dependent variables 583
82. Computer generation of random vectors based on transformation of uniformly distributed vectors 589
83. III. Operations Research and Mathematical Programming
84. A generative picture processing device used in two-dimensional cutting problems 599
85. The world nuclear weapons system is self-activating 607
86. Ein Differentialspiel zu Goethes Faust 615
87. Efficiency of some approximate implicit enumeration algorithms 623
88. General stochastic games 643
89. IV. Biomathematics
90. On a general classification problem 649
91. Which factors influence the course of acute leukaemia in adults? A stochastic approach 655
92. Estimation of non-measurable state variables in biotechnical processes 663
93. LIST OF PARTICIPANTS 669