Ergodicity and asymptotic behaviour of multi-type branching processes arising in random-access communication systems

Chapters in this book

1. Frontmatter I
2. Contents V
3. Preface XV
4. Greeting XVII
5. Opening Talk
6. Algorithms And Randomness 3
7. Self Similar Processes In Probability Theory And Statistics (Session 9 - Chairman: Ya.G. Sinay)
8. INVITED PAPERS
9. Limit theorems in statistical physics; on Dyson's hierarchical model 57
10. Statistical aspects of self-similar processes 67
11. Toeplitz matrices and estimation of time series with long-range dependence 75
12. Contributed Papers
13. Universal behavior and stochasticity for one dimensional systems 85
14. A birth and death process in random environment 91
15. Spectral properties of some finite-difference and differential operators with random coefficients 95
16. Point Processes In Probability Theory And Statistics (Session 10 - Chairman: D. Stoyan)
17. Invited Papers
18. Parametric and non-parametric estimation for pairwise-interaction point processes 101
19. On the theory of conditioning in point processes 113
20. Contributed Papers
21. On The Exponentiality Of Total Hazards Before Failure 123
22. Sufficient regularity conditions for jump processes 127
23. Statistics with diffusion crossing times 131
24. Ruin probabilities in the "non-renewal" case 135
25. A note on the asymptotic behaviour of the empirical score in Cox's regression model for counting processes 139
26. Comparison of Cox's and maximum likelihood estimates for matched experiments in survival data with censoring 143
27. On the conditions providing for the moments of number of zeros of a vector Gaussian field to be finite 147
28. The inverses of thinned point processes 151
29. Foundations Of Probability Theory (Session 17 - Chairman: D. Lane)
30. Invited Papers
31. An epistemic justification of the law of total probability 155
32. Contributed Papers
33. Individual Random Continuous Functions 169
34. Some Estimates For Nonstochastic Sequences 173
35. Nonstandard Analysis In Probability Theory (Session 19 - Chairman: E. Perkins)
36. Invited Papers
37. Nonstandard Constructions Of Diffusions And Related Processes 179
38. Nonstandard analysis in probability theory 191
39. Contributed Papers
40. Adapted distribution 201
41. Hyperfinite methods for multidimensional stochastic processes 205
42. Combinatorial Methods In Probability Theory (Session 20 - Chairman: B.S. Stechkin)
43. Invited Papers
44. Random mappings and branching processes 211
45. On probability methods in combinatorial analysis 219
46. Contributed Papers
47. Neighbourhood Spaces And Maps 227
48. Percolation theory. Coincidence of the critical values P_H = P_T 231
49. Evolution on random mappings 235
50. On the distribution of the number of vertices in strata of a random forest 239
51. Queing Theory (Network, Computer-User Models, Stability ...) (Session 22 - Chairman: R. Schassberger)
52. Invited Papers
53. Stationary queueing systems. Existence and stability 245
54. Ergodicity and asymptotic behaviour of multi-type branching processes arising in random-access communication systems 261
55. Insensitive service schemes and partial balance 271
56. Contributed Papers
57. Queueing networks and operator-selfdecomposability 279
58. Insensitivity in queueing networks with generalized processor-sharing discipline 283
59. Markov Processes (Session 24 - Chairman: Y. Le Jan)
60. Invited Papers
61. Intrinsic properties of Markov processes 289
62. Reversible diffusion processes on manifolds 297
63. The entropy production and reversibility of Markov processes 307
64. Contributed Papers
65. The theory of shuffling - an application of non-homogeneous Markov chains 317
66. Asymptotic periodicity of the iterates of Markov operators 321
67. Homogeneous transition functions and dual semigroups 327
68. On the arcsine law in the adaptive control of Markov chains 331
69. Random Fields And Percolation Theory (Session 25 - Chairman: Y. Higuchi)
70. Invited Papers
71. Random sets and Markov fields 339
72. Central limit results for random fields 345
73. Recent progress in percolation 353
74. Contributed Papers
75. Uniqueness of Gibbs measures and absorption probabilities 359
76. A decomposition theorem for binary Markov random fields 361
77. Percolation problem for the two-dimensional Ising model 363
78. Probabilistic models of the growth of epithelial tumors 367
79. On the homogenization error for boundary problems with highly oscillating random coefficients 371
80. Time Evolution Of Particle Systems (Session 26 - Chairman: T. Liggett)
81. Invited Papers
82. Switching networks, Markov interaction processes, Gibbsian fields - interconnection 377
83. Collective behaviour of interacting particle systems 395
84. Contributed Papers
85. The supremum of a random walk in a Markovian environment 415
86. Dynamics of infinite particle systems and Gibbs point random fields 419
87. The Euler equations for the one-dimensional zero range process 423
88. Probability And Theoretical Physics (Session 27 - Chairman: K.R. Parthasarathy)
89. Invited Papers
90. Recent developments in quantum probability 427
91. Markov operators on quantum probability spaces 445
92. Some recent interactions between mathematics and physics in connection with generalized random fields 455
93. Contributed Papers
94. Non-commutative point processes and quantum kinetic equations 473
95. Quantum diffusions and cohomology of algebras 479
96. Quantum stochastic calculus with integral kernels I 485
97. Quantum stochastic calculus with integral kernels II: the Wigner-Weisskopf atom 491
98. Stop Times in Fock Space Stochastic Calculus 495
99. Diffusion On Manifolds (Session 28 - Chairman: K.D. Elworthy)
100. Invited Papers
101. Some Geometric Aspects Of Diffusions On Manifolds 501
102. Stochastic Differential Geometry 515
103. Contributed Papers
104. Stochastic equations on Banach manifolds and bundles 525
105. Brownian motion in a small ball 529
106. Stochastic Calculus (Including Malliavin Calculus) (Session 29 - Chairman: J. Bismut)
107. Invited Papers
108. Stochastic quantization: A new domain for stochastic analysis 535
109. Some intersection properties of Brownian paths and random walks 547
110. Malliavin calculus and its application to some limit theorems 557
111. Contributed Papers
112. Probabilistic method of approach to certain problems of Fourier analysis 567
113. On sufficient conditions for the convergence of solutions of stochastic equations 571
114. Martingales with mixed norm: general theory and applications 575
115. Convergence in probability for solutions of stochastic differential equations 579
116. Some remarks on approximation of predictable characteristics of processes with filtrations 583
117. Stochastic Geometry (Session 30 - Chairman: J. Mecke)
118. Invited Papers
119. Stochastic approximations of convex bodies by polyhedrons 589
120. Symmetric statistics and random shape 595
121. Point processes of compact sets 601
122. Contributed Papers
123. A brief account of the structure and explicit determination of convex-polygonally generated shape-densities 611
124. On homogeneous processes of lines in the plane 615
125. Intersections of random curves and surfaces 619
126. Random curvature currents and generalized Regge calculus 623
127. Large Deviations (Session 31 - Chairman: A.A. Borovkov)
128. Invited Papers
129. Theorems of large deviations for multinomial forms and multiple stochastic integrals 629
130. Global exact asymptotics of large deviations probabilities for diffusion and jump processes 641
131. Contributed Papers
132. Large deviations and long-time behavior of stochastic particle systems 651
133. Random perturbations of infinite dimensional dynamical systems 655
134. Large deviations estimates for systems with small (wideband) noise effects and applications to stochastic systems and conmunication theory 659
135. On the Donsker-Varadhan theory and its applications 663
136. Rates Of Convergence (Session 32 - Chairman: F. Götze)
137. Invited Papers
138. Approximations in functional limit theorems 669
139. Asymptotic expansions refining the central limit theorem in Hilbert space 679
140. Contributed Papers
141. Estimates of the rate of convergence in the local limit theorem for countable Markov chains 689
142. On asymptotic expansion for the distribution of the sum of independent identically distributed random variables taking values in Hilbert space 693
143. On the uniform approximation of distribution functions of sums of independent non-identically distributed random variables 697
144. Functional Limit Theorems: An Invariance Principle (Session 33 - Chairman: Yu.V. Prohorov)
145. Invited Papers
146. On accuracy of approximation in invariance principle 703
147. Contributed Papers
148. On strong convergence of distributions of random process functionals 713
149. Almost sure invariance principles for generalization of martingales 717
150. On the rate of convergence in ordinary and functional central limit theorems for martingales 721
151. Probabilities On Algebraic Structures (Session 34 - Chairman: V.M. Maksimov)
152. Invited Papers
153. Generalized convolutions and probability theory based on the q-Heisenberg algebra 729
154. Asymptotic behaviour of products of random matrices 743
155. Lie algebraic methods in filtering and identification 749
156. Contributed Papers
157. Limit theorem for products of dependence 767
158. Random series and seminorms 771
159. Miscellaneous (Session 35)
160. Contributed Papers
161. On the maximum principle for stochastic control problems 777
162. Stochastic scheduling via stochastic control 783
163. A de Finetti theorem for a class of pairwise independent stationary processes 789
164. Computer application in the teaching process at the institute of economics 793
165. Probabilistic derivation of inversion formulas 797