Stability Problems for Stochastic Models: Proceedings of the International Seminar, held in Suzdal, Russia, Jan. 27–Feb. 2, 1991

Caterina Dimaki, Evdokia Xekalaki (auth.), Vladimir V. Kalashnikov, Vladimir M. Zolatarev (eds.)9780387567440, 0-387-56744-5, 3540567445

The subject of this book is a new direction in the field of probability theory and mathematical statistics which can be called “stability theory”: it deals with evaluating the effects of perturbing initial probabilistic models and embraces quite varied subtopics: limit theorems, queueing models, statistical inference, probability metrics, etc. The contributions are original research articles developing new ideas and methods of stability analysis.

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Table of contents :
Characterizations of the pareto distribution based on order statistics….Pages 1-16
Some characterizations of the exponential distribution based on the service time properties of an unreliable server….Pages 17-25
On the distribution of the Wilcoxon Rank-Sum statistic….Pages 26-32
On different stability-concepts for probabilities on groups….Pages 33-44
Functional limit theorems for random walks on one-dimensional hypergroups….Pages 45-57
Stabilities and instabilities in population dynamics….Pages 58-67
Some properties of random variables which are stable with respect to the random sample size….Pages 68-75
Two-side estimates of geometric convolutions….Pages 76-88
A stochastic model of radiation carcinogenesis….Pages 89-99
Limit theorems for random sums of independent random variables….Pages 100-120
On regularly varying multivalued functions….Pages 121-129
A comparison theorem for queueing system with non-identical channels….Pages 130-133
On an intrinsic bias measure….Pages 134-158
Characterization of exponential distributions by conditional moments….Pages 159-162
The functional limit theorem on nilpotent lie group….Pages 163-166
On wide-sense regeneration….Pages 167-169
Some properties of the median of the stable distributions close to the symmetric ones….Pages 170-173
Regeneration, stationarity and simulation….Pages 174-179
Multivariate infinitely divisible distributions with the gaussian second order conditional structure….Pages 180-183
On the convergence of random symmetric polynomials….Pages 184-188
Stability of characterization by record properties….Pages 189-196
A berry – esséen bound for multivariate l-estimates with explicit dependence on dimension….Pages 197-211
On the ergodicity condition of random walks with a periodic control sequence….Pages 212-223
Some limit problem for dependent random variables….Pages 224-229