Stability Problems for Stochastic Models: Proceedings of the 11th International Seminar held in Sukhumi (Abkhazian Autonomous Republic) USSR, Sept. 25–Oct. 1, 1987

S. V. Arkhipov (auth.), Vladimir V. Kalashnikov, Vladimir M. Zolotarev (eds.)9780387519487, 0-387-51948-3

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.

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Table of contents :
The density function’s asymptotic representation in the case of multidimensional strictly stable distributions….Pages 1-21
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….Pages 22-32
On the adaptive estimation of change points….Pages 33-49
Precise upper bounds for the functionals describing tumour treatment efficiency….Pages 50-67
A multivariate analog of the Cramer theorem on components of the Gaussian distributions….Pages 68-77
A refinement of Lukacs theorems….Pages 78-82
On the connection of Renyi’s theorem and Renewal theory….Pages 83-102
On the products of a random number of random variables in connection with a problem from mathematical economics….Pages 103-109
The asymptotic distributions of random sums….Pages 110-123
Normal and degenerate convergences of random sums….Pages 124-136
New duality theorems for Marginal problems with some applications in stochastics….Pages 137-171
Stable random vectors in Hilbert space….Pages 172-182
The mean’s consistent estimation, in the case random processes, satisfying partial differential equations….Pages 183-193
Limit theorems in the set up of sumnation of a random number of independent identically distributed random variables….Pages 194-228
Some asymptotic properties of the stable laws….Pages 229-238
A chi-square goodness-of-fit test for exponential distributions of the first order….Pages 239-258
A conditional weak law of large numbers….Pages 259-262
On the rate of convergence for the extreme value in the case of IFR-distributions….Pages 263-269
On the rate of convergence in extreme value theory….Pages 270-279
Some properties of stochastic processes with linear regression….Pages 280-287
On characterization of generalized logistic and pareto distributions….Pages 288-295
Limit theorems for positive definite probability densities….Pages 296-308
On the estimate of the rate of convergence in the central limit theorem in Hilbert space….Pages 309-327
Stability of decomposition in semigroups of functions representable by series in the Jacobi polynomials….Pages 328-348
A regressional characterization of the poisson distribution….Pages 349-351
Hitting times of single points for 1-dimensional generalized diffusion processes….Pages 352-359
Pseudotrajectories and stability problems for stochastic dynamical systems….Pages 360-380