V. Yu. Korolev, “Convergence of random sequences with the independent random indices. I”, Teor. Veroyatnost. i Primenen., 39:2 (1994), 313–333; Theory Probab. Appl., 39:2 (1994), 282

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Teoriya Veroyatnostei i ee Primeneniya, 1994, Volume 39, Issue 2, Pages 313–333 (Mi tvp3804)

This article is cited in 40 scientific papers (total in 40 papers)

Convergence of random sequences with the independent random indices. I

V. Yu. Korolev

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Full-text PDF (1219 kB) Citations (40)

Abstract: Necessary and sufficient conditions are obtained for the weak convergense of arbitrary random sequences with independent random indices under nonrandom centering and normalization. The relationship between these conditions and the concept of identifiability of families of probability distributions is traced back. As particular cases,. the conditions for the convergence of “growing” random sums and maximum partial random sums are given.

Keywords: random sequences with random indices, weak convergence, tightness, location mixtures, scale mixtures, identifiable mixtures, random sums.

Received: 13.09.1993

English version:
Theory of Probability and its Applications, 1994, Volume 39, Issue 2, Pages 282–297
DOI: https://doi.org/10.1137/1139018

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. Yu. Korolev, “Convergence of random sequences with the independent random indices. I”, Teor. Veroyatnost. i Primenen., 39:2 (1994), 313–333; Theory Probab. Appl., 39:2 (1994), 282–297

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tvp3804

https://www.mathnet.ru/eng/tvp/v39/i2/p313

Cycle of papers

Convergence of random sequences with the independent random indices. I
V. Yu. Korolev
Teor. Veroyatnost. i Primenen., 1994, 39:2, 313–333
Convergence of random sequences with independent random indices. II
V. Yu. Korolev
Teor. Veroyatnost. i Primenen., 1995, 40:4, 907–910

This publication is cited in the following 40 articles:

V. Yu. Korolev, I. G. Shevtsova, O. V. Shestakov, “Asymptotic and Analytic Properties of Mixture Probability Models and Their Application to the Analysis of Complex Systems”, MoscowUniv.Comput.Math.Cybern., 48:4 (2024), 317
Gorshenin A. Kuzmin V., “Statistical Feature Construction For Forecasting Accuracy Increase and Its Applications in Neural Network Based Analysis”, Mathematics, 10:4 (2022), 589
Victor Korolev, “Bounds for the Rate of Convergence in the Generalized Rényi Theorem”, Mathematics, 10:22 (2022), 4252
N. A. Slepov, “Convergence rate of random geometric sum distributions to the Laplace law”, Theory Probab. Appl., 66:1 (2021), 121–141
Korolev V. Zeifman A., “Bounds For Convergence Rate in Laws of Large Numbers For Mixed Poisson Random Sums”, Stat. Probab. Lett., 168 (2021), 108918
V. Yu. Korolev, “O raspredelenii otnosheniya summy elementov vyborki, prevoskhodyaschikh nekotoryi porog, k summe vsekh elementov vyborki. I”, Inform. i ee primen., 14:3 (2020), 35–43
Gorshenin A. Korolev V. Zeifman A., “Modeling Particle Size Distribution in Lunar Regolith Via a Central Limit Theorem For Random Sums”, Mathematics, 8:9 (2020), 1409
Korolev V., Gorshenin A., “Probability Models and Statistical Tests For Extreme Precipitation Based on Generalized Negative Binomial Distributions”, Mathematics, 8:4 (2020), 604
Victor Korolev, Alexander Zeifman, Probability, Combinatorics and Control, 2020
Korolev V.Yu. Zeifman A.I., “Generalized Negative Binomial Distributions as Mixed Geometric Laws and Related Limit Theorems”, Lith. Math. J., 59:3 (2019), 366–388
Korolev V. Gorshenin A. Belyaev K., “Statistical Tests For Extreme Precipitation Volumes”, Mathematics, 7:7 (2019), 648
V. Yu. Korolev, A. K. Gorshenin, A. I. Zeifman, “Novye predstavleniya obobschennogo raspredeleniya Mittag-Lefflera v vide smesei i ikh prilozheniya”, Inform. i ee primen., 12:4 (2018), 75–85
V. Yu. Korolev, “Nekotorye svoistva raspredeleniya Mittag-Lefflera i svyazannykh s nim protsessov”, Inform. i ee primen., 11:4 (2017), 26–37
Korolev V.Yu. Zeifman A.I., “Convergence of Statistics Constructed From Samples With Random Sizes to the Linnik and Mittag-Leffler Distributions and Their Generalizations”, J. Korean Stat. Soc., 46:2 (2017), 161–181
Korolev V. Gorshenin A. Korchagin A. Zeifman A., “Generalized Gamma Distributions as Mixed Exponential Laws and Related Limit Theorems”, Proceedings of the 31st European Conference on Modelling and Simulation (ECMS 2017), ed. Paprika Z. Horak P. Varadi K. Zwierczyk P. VidovicsDancs A. Radics J., European Council Modelling & Simulation, 2017, 642–648
H. Bevrani, V. Yu. Korolev, “Estimation of availability function using Student distribution”, Theory Probab. Appl., 61:2 (2017), 327–335
V. Yu. Korolev, “Limit distributions for doubly stochastically rarefied renewal processes and their properties”, Theory Probab. Appl., 61:4 (2017), 649–664
V. Yu. Korolev, A. I. Zeifman, A. Yu. Korchagin, “Nesimmetrichnye raspredeleniya Linnika kak predelnye zakony dlya sluchainykh summ nezavisimykh sluchainykh velichin s konechnymi dispersiyami”, Inform. i ee primen., 10:4 (2016), 21–33
Korolev V.Yu. Zeifman A.I., “On convergence of the distributions of random sequences with independent random indexes to variance–mean mixtures”, Stoch. Models, 32:3 (2016), 414–432
Korolev V.Yu. Chertok A.V. Korchagin A.Yu. Zeifman A.I., “Modeling High-Frequency Order Flow Imbalance By Functional Limit Theorems For Two-Sided Risk Processes”, Appl. Math. Comput., 253 (2015), 224–241

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Theory of Probability and its Applications

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