V. M. Zolotarev, “On representation of densities of stable laws by special functions”, Teor. Veroyatnost. i Primenen., 39:2 (1994), 429–437; Theory Probab. Appl., 39:2 (1994), 354

Teoriya Veroyatnostei i ee Primeneniya

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Guidelines for authors
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Teoriya Veroyatnostei i ee Primeneniya, 1994, Volume 39, Issue 2, Pages 429–437 (Mi tvp3812)

This article is cited in 28 scientific papers (total in 28 papers)

Short Communications

On representation of densities of stable laws by special functions

V. M. Zolotarev

Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (533 kB) Citations (28)

Abstract: A representation of the density of a one-dimensional strongly stable law via Meijer's

G

$G$ -functions is obtained. The paper also considers the expressions of integral transforms with Euler kernels of these densities in terms of

G

$G$ -functions which make it possible to obtain representations of distribution functions of strongly stable laws with rational parameters. Some examples are given of representations of densities of multivariate spherically symmetric stable laws in terms of Meijer functions.

Keywords: one-dimensional strongly stable laws, multivariate spherically symmetric stable distributions, higher transcendental functions, generalized hypergeometrical series, Meijer's

G

$G$ -functions.

Received: 21.11.1993

English version:
Theory of Probability and its Applications, 1994, Volume 39, Issue 2, Pages 354–362
DOI: https://doi.org/10.1137/1139025

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. M. Zolotarev, “On representation of densities of stable laws by special functions”, Teor. Veroyatnost. i Primenen., 39:2 (1994), 429–437; Theory Probab. Appl., 39:2 (1994), 354–362

Citation in format AMSBIB

\Bibitem{Zol94}

\by V.~M.~Zolotarev

\paper On representation of densities of stable laws by special functions

\jour Teor. Veroyatnost. i Primenen.

\yr 1994

\vol 39

\issue 2

\pages 429--437

\mathnet{http://mi.mathnet.ru/tvp3812}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1404693}

\zmath{https://zbmath.org/?q=an:0872.60012}

\transl

\jour Theory Probab. Appl.

\yr 1994

\vol 39

\issue 2

\pages 354--362

\crossref{https://doi.org/10.1137/1139025}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995RW81500014}

Linking options:

https://www.mathnet.ru/eng/tvp3812

https://www.mathnet.ru/eng/tvp/v39/i2/p429

This publication is cited in the following 28 articles:

Guangyao Zhang, Yi Wang, Yi Qin, Baoping Tang, “Statistical distribution measures based on amplitude normalization for wind turbine generator bearing condition monitoring under variable speed conditions”, Mechanical Systems and Signal Processing, 228 (2025), 112464
Gero Junike, “On the number of terms in the COS method for European option pricing”, Numer. Math., 156:2 (2024), 533
Thomas Mikosch, Olivier Wintenberger, Springer Series in Operations Research and Financial Engineering, Extreme Value Theory for Time Series, 2024, 33
Viacheslav V. Saenko, “The Calculation of the Probability Density and Distribution Function of a Strictly Stable Law in the Vicinity of Zero”, Mathematics, 10:20 (2022), 3861
Viacheslav Saenko, “The Calculation of the Density and Distribution Functions of Strictly Stable Laws”, Mathematics, 8:5 (2020), 775
J.C. Crisanto-Neto, M.G.E. da Luz, E.P. Raposo, G.M. Viswanathan, “An efficient series approximation for the Lévy α -stable symmetric distribution”, Physics Letters A, 382:35 (2018), 2408
Han-Xiong Li, Yan Wang, Geng Zhang, “Probabilistic Fuzzy Classification for Stochastic Data”, IEEE Trans. Fuzzy Syst., 25:6 (2017), 1391
Mahdi Louati, Afif Masmoudi, Farouk Mselmi, “Multivariate Normal α-Stable Exponential Families”, Mediterr. J. Math., 13:3 (2016), 1307
Marcin Magdziarz, Tomasz Zorawik, “Densities of Scaling Limits of Coupled Continuous Time Random Walks”, FCAA, 19:6 (2016), 1488
Advances in Heavy Tailed Risk Modeling, 2015, 597
Tibor K. Pogány, Saralees Nadarajah, “Remarks on the Stable S α (β,γ,μ) Distribution”, Methodol Comput Appl Probab, 17:2 (2015), 515
Simon T., “Comparing Frechet and Positive Stable Laws”, Electron. J. Probab., 19 (2014), 16, 1–25
D. O'Malley, V.V. Vesselinov, “Analytical solutions for anomalous dispersion transport”, Advances in Water Resources, 68 (2014), 13
A. Provata, E. Panagakou, “Abstract phase space networks describing reactive dynamics”, Physica A: Statistical Mechanics and its Applications, 414 (2014), 181
Yunfei Chen, Feng Xu, Jiming Chen, “Polynomial‐approximation‐based locally optimum detector for signals with symmetric alpha stable noise”, IET Communications, 8:16 (2014), 2952
Marc Hallin, Yvik Swan, Thomas Verdebout, David Veredas, “One-step R-estimation in linear models with stable errors”, Journal of Econometrics, 172:2 (2013), 195
Yacine Aït-Sahalia, Jean Jacod, “Identifying the successive Blumenthal–Getoor indices of a discretely observed process”, Ann. Statist., 40:3 (2012)
Nizar Demni, “Kanter random variable and positive free stable distributions”, Electron. Commun. Probab., 16:none (2011)
Marc Hallin, Yvik Swan, Thomas Verdebout, David Veredas, “Rank-based testing in linear models with stable errors”, Journal of Nonparametric Statistics, 23:2 (2011), 305
Marc Hallin, Yvik Swan, Thomas Verdebout, David Veredas, “One-Step R-Estimation in Linear Models with Stable Errors”, SSRN Journal, 2010

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

Theory of Probability and its Applications

Statistics & downloads:
Abstract page:	576
Full-text PDF :	176
First page:	47

Registration to the website

Logotypes