V. Yu. Korolev, “On convergence of distributions of compound Cox processes to stable laws”, Teor. Veroyatnost. i Primenen., 43:4 (1998), 786–792; Theory Probab. Appl., 43:4 (1999), 644

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Teoriya Veroyatnostei i ee Primeneniya, 1998, Volume 43, Issue 4, Pages 786–792
DOI: https://doi.org/10.4213/tvp2080 (Mi tvp2080)

This article is cited in 22 scientific papers (total in 22 papers)

Short Communications

On convergence of distributions of compound Cox processes to stable laws

V. Yu. Korolev

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

Full-text PDF (1116 kB) Citations (22)

DOI: https://doi.org/10.4213/tvp2080

Abstract: Necessary and sufficient conditions are presented for weak convergence of one-dimensional distributions of compound doubly stochastic Poisson processes in which jumps have finite variances, whereas no moment-type restrictions are imposed on the controlling process. Criteria of convergence of distributions of these processes to stable laws are presented.

Keywords: doubly stochastic Poisson process (Cox process), compound Cox process, heavy tails, strictly stable distribution.

Received: 13.11.1997

English version:
Theory of Probability and its Applications, 1999, Volume 43, Issue 4, Pages 644–650
DOI: https://doi.org/10.1137/S0040585X97977227

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. Yu. Korolev, “On convergence of distributions of compound Cox processes to stable laws”, Teor. Veroyatnost. i Primenen., 43:4 (1998), 786–792; Theory Probab. Appl., 43:4 (1999), 644–650

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tvp2080

https://doi.org/10.4213/tvp2080

https://www.mathnet.ru/eng/tvp/v43/i4/p786

This publication is cited in the following 22 articles:

Victor Yu. Korolev, “The Logistic Distribution as a Limit Law for Random Sums and Statistics Constructed from Samples with Random Sizes”, Mathematics, 12:23 (2024), 3775
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
Victor Korolev, “Analytic and Asymptotic Properties of the Generalized Student and Generalized Lomax Distributions”, Mathematics, 11:13 (2023), 2890
Korolev V. Zeifman A., “Bounds For Convergence Rate in Laws of Large Numbers For Mixed Poisson Random Sums”, Stat. Probab. Lett., 168 (2021), 108918
Oliveira G. Barreto-Souza W. Silva R.W.C., “Convergence and Inference For Mixed Poisson Random Sums”, Metrika, 84:5 (2021), 751–777
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
A. K. Gorshenin, V. Yu. Korolev, “Scale Mixtures of Frechet Distributions as Asymptotic Approximations of Extreme Precipitation”, J Math Sci, 234:6 (2018), 886
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
Victor Korolev, Andrey Chertok, Alexander Korchagin, Alexander Zeifman, “Modeling High-Frequency Order Flow Imbalance by Functional Limit Theorems for Two-Sided Risk Processes”, SSRN Journal, 2014
Andrey Chertok, Victor Korolev, Alexander Korchagin, Sergey Shorgin, “Application of Compound Cox Processes In Modeling Order Flows with Non-Homogeneous Intensities”, SSRN Journal, 2014
V. Yu. Korolev, L. M. Zaks, A. I. Zeifman, “O skhodimosti sluchainykh bluzhdanii, porozhdennykh obobschennymi protsessami Koksa, k protsessam Levi”, Inform. i ee primen., 7:2 (2013), 84–91
Korolev V.Yu. Zaks L.M. Zeifman A.I., “On Convergence of Random Walks Generated by Compound Cox Processes to Levy Processes”, Stat. Probab. Lett., 83:10 (2013), 2432–2438
S. V. Gavrilenko, V. Yu. Korolev, “Otsenki skorosti skhodimosti smeshannykh puassonovskikh sluchainykh summ”, Sistemy i sredstva inform., 2006, spetsvypusk, 248–257
N. N. Skvortsova, V. Yu. Korolev, T. A. Maravina, G. M. Batanov, A. E. Petrov, A. A. Pshenichnikov, K. A. Sarksyan, N. K. Kharchev, J. Sanchez, S. Kubo, “New possibilities for the mathematical modeling of turbulent transport processes in plasma”, Plasma Phys. Rep., 31:1 (2005), 57
Ng K.W., Tang Q.H., Yan J.A., Yang H.L., “Precise large deviations for sums of random variables with consistently varying tails”, Journal of Applied Probability, 41:1 (2004), 93–107
Tang Q.H., “Uniform estimates for the tail probability of maxima over finite horizons with subexponential tails”, Probability in the Engineering and Informational Sciences, 18:1 (2004), 71–86
Kai W. Ng, Qihe Tang, Jia-An Yan, Hailiang Yang, “Precise large deviations for sums of random variables with consistently varying tails”, J. Appl. Probab., 41:01 (2004), 93
V. E. Bening, V. Yu. Korolev, “Nonparametric Estimation of the Ruin Probability for Generalized Risk Processes”, Theory Probab. Appl., 47:1 (2003), 1

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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