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Teoriya Veroyatnostei i ee Primeneniya, 2021, Volume 66, Issue 1, Pages 149–174
DOI: https://doi.org/10.4213/tvp5363 (Mi tvp5363) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Convergence rate of random geometric sum distributions to the Laplace law

N. A. Slepov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (515 kB) Citations (5)
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DOI: https://doi.org/10.4213/tvp5363
Abstract: In this paper we modify the Stein method and the auxiliary technique of distributional transformations of random variables. This enables us to estimate the convergence rate of distributions of normalized geometric sums to the Laplace law. For independent summands, the developed approach provides an optimal estimate involving the ideal metric of order 3. New results are also obtained for the Kolmogorov and Kantorovich metrics.
Keywords: Stein's method, geometric random sum, zero-bias transform, equilibrium transform, convergence rate to the Laplace distribution, analogue of the Berry–Esseen inequality, optimal estimate.
Funding agency Grant number
Lomonosov Moscow State University
This work was supported by the grant “Modern Problems of Fundamental Mathematics and Mechanics” at Lomonosov Moscow State University.
Received: 08.10.2019
Revised: 02.09.2020
Accepted: 04.08.2020
English version:
Theory of Probability and its Applications, 2021, Volume 66, Issue 1, Pages 121–141
DOI: https://doi.org/10.1137/S0040585X97T990290
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: N. A. Slepov, “Convergence rate of random geometric sum distributions to the Laplace law”, Teor. Veroyatnost. i Primenen., 66:1 (2021), 149–174; Theory Probab. Appl., 66:1 (2021), 121–141
Citation in format AMSBIB
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\paper Convergence rate of random geometric sum distributions to the Laplace law
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\transl
\jour Theory Probab. Appl.
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\pages 121--141
\crossref{https://doi.org/10.1137/S0040585X97T990290}
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  • https://www.mathnet.ru/eng/tvp/v66/i1/p149
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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