Stability problems for stochastic models : proceedings of the 11th International Seminar held in Sukhumi (Abkhazian Autonomous Republic) USSR, Sept. 25-Oct. 1, 1987

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Stability problems for stochastic models : proceedings of the 11th International Seminar held in Sukhumi (Abkhazian Autonomous Republic) USSR, Sept. 25-Oct. 1, 1987

V.V. Kalashnikov, V.M. Zolotarev (eds.)

（Lecture notes in mathematics, 1412）

Springer-Verlag, c1989

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  • : us

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Translated from the Russian

"An International Seminar on Stability Problems for Stochastic Models was held in Sukhumi (Abkhasian Autonomic Republic) from 25 September till 1 October 1987. This seminar was the eleventh since the Steklov Mathematical Institute USSR Acad. Sci. launched them ... The Institute for Systems Studies (ISS) is a permanent co-organizer of these seminars" -- Introd

Includes bibliographical references

Description and Table of Contents

Description

Traditionally the Stability seminar, organized in Moscow but held in different locations, has dealt with a spectrum of topics centering around characterization problems and their stability, limit theorems, probabil- ity metrics and theoretical robustness. This volume likewise focusses on these main topics in a series of original and recent research articles.

Table of Contents

The density function's asymptotic representation in the case of multidimensional strictly stable distributions.- Limiting behaviour of the sum of I.I.D. random variables and its terms of greatest moduli in the case of logarithmic type tall function.- On the adaptive estimation of change points.- Precise upper bounds for the functionals describing tumour treatment efficiency.- A multivariate analog of the Cramer theorem on components of the Gaussian distributions.- A refinement of Lukacs theorems.- On the connection of Renyi's theorem and Renewal theory.- On the products of a random number of random variables in connection with a problem from mathematical economics.- The asymptotic distributions of random sums.- Normal and degenerate convergences of random sums.- New duality theorems for Marginal problems with some applications in stochastics.- Stable random vectors in Hilbert space.- The mean's consistent estimation, in the case random processes, satisfying partial differential equations.- Limit theorems in the set up of sumnation of a random number of independent identically distributed random variables.- Some asymptotic properties of the stable laws.- A chi-square goodness-of-fit test for exponential distributions of the first order.- A conditional weak law of large numbers.- On the rate of convergence for the extreme value in the case of IFR-distributions.- On the rate of convergence in extreme value theory.- Some properties of stochastic processes with linear regression.- On characterization of generalized logistic and pareto distributions.- Limit theorems for positive definite probability densities.- On the estimate of the rate of convergence in the central limit theorem in Hilbert space.- Stability of decomposition in semigroups of functions representable by series in the Jacobi polynomials.- A regressional characterization of the poisson distribution.- Hitting times of single points for 1-dimensional generalized diffusion processes.- Pseudotrajectories and stability problems for stochastic dynamical systems.

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