Stability Problems for Stochastic Models Proceedings of the 9th Inte
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Stability Problems for Stochastic Models Proceedings of the 9th International Seminar held in Varna, Bulgaria, May 13-19, 1985
Edited by V.V. Kalashnikov, B. Penkovand V. M. Zolotarev
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Editors Vladimir V. Kalashnikov Institute for System Studies Prospekt 60 let Oktjabrja 9 117312 Moscow, USSR Boyan Penkov Bulgarian Academy of Sciences Centre for Mathematics and Mechanics P.O. Box 373 1090 Sofia, Bulgaria Vladimir M. Zolotarev Steklov Mathematical Institute. Academy of Sciences of the USSR Vavilov st. 42, 117333 Moscow, USSR
Mathematics Subject Classification (1980): 60B 10, 60B99, 60E 10, 60E99, 60F05, 60K25, 60K99, 62E 10, 62F 10, 62F35, 62H 12, 62P99 ISBN 3-540-17204-1 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-17204-1 Springer-Verlag New York Berlin Heidelberg
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© Springer-Verlag Berlin Heidelberg 1987 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210
CON TEN T S
Page
Zolotarev, V.M.
Preface
1. Hohlov, Yu. S. The estimation of the rate of convergence in the integral limit theorem in the Euclidean motion group 2. Kagan, A.M., Zinger, A.A., Contribution to the analytic theory of forms of independent random variables
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3. Klebanov, L.B., Manija, G.M., Melamed, J.A. stable laws and estImatIon of their parameters • • . . . . . . . . . • . . .. 23 4. Koicheva, M. The method of metric distances in the problem of estimation of deviation from the exponential distribution .......•.......................•••.•.............. 32 5. Korolev, V.Yu. The accuracy of the normal approximation to the distribution of the sum of a random number of independent random variables .............•....•..•................ 36 Kruglov, V.M., Titov, A.N. Mixtures of probability distributions .....•.......................•••................. 41 7. Maejima, M. Some limit theorems for summability methods of LLd. random variables .........•.....••.•.•............... 57 8. Nagaev, A.V., Shcolnick, S.M. Properties of mode of spectral positive stable distributions ..••.................... 69 9. Nevzorov, V.B. Two characterizations using records
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10. Nikulin, V.N. On orthogonal-series estimators for probability distributions .............••.•••.•..•............. 86 11. Obretov, A., Rachev, S. Estimates of the deviation between the exponential and new classes of bivariate distributions ....................••..•••••.•.•.•••........•... 93 12. Omey, E., Willekens, E. On the difference between distributions of sums and maxima ....•••.•••.•.•......•......•• 103 13. Popov, V.A. On the inequalities
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