Fractional Edgeworth expansions for one-dimensional heavy-tailed random variables and applications

Leandro Chiarini Medeiros; Milton Jara; Wioletta Ruszel

doi:10.1214/23-EJP996

Fractional Edgeworth expansions for one-dimensional heavy-tailed random variables and applications

Leandro Chiarini Medeiros
, Milton Jara
, Wioletta Ruszel

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

In this article, we study a class of lattice random variables in the domain of attraction of an α-stable random variable with index α ∈ (0, 2) which satisfy a truncated fractional Edgeworth expansion. Our results include studying the class of such fractional Edgeworth expansions under simple operations, providing concrete examples; sharp rates of convergence to an α-stable distribution in a local central limit theorem; Green’s function expansions; and finally fluctuations of a class of discrete stochastic PDE’s driven by the heavy-tailed random walks belonging to the class of fractional Edgeworth expansions.

Original language	English
Article number	108
Pages (from-to)	1-42
Number of pages	42
Journal	Electronic Journal of Probability
Volume	28
DOIs	https://doi.org/10.1214/23-EJP996
Publication status	Published - 29 Aug 2023

Bibliographical note

Publisher Copyright:
© 2023, Institute of Mathematical Statistics. All rights reserved.

Funding

*L. Chiarini was financially supported by CAPES and the NWO grant OCENW.KLEIN.083. M. Jara was funded by the ERC Horizon 2020 grant 715734, the CNPq grant 305075/2017-9 and the FAPERJ grant E-29/203.012/201. W. M. Ruszel is funded by OCENW.KLEIN.083 and the Vidi grant VI.Vidi.213.112 from the Dutch Research Council.

Funders	Funder number
ERC Horizon 2020	715734
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Nederlandse Organisatie voor Wetenschappelijk Onderzoek	OCENW.KLEIN.083
Conselho Nacional de Desenvolvimento Científico e Tecnológico	305075/2017-9
Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro	VI.Vidi.213.112, E-29/203.012/201

Keywords

discrete stochastic linear stochastic equations
fluctuations
fractional Edgeworth expansion
heavy-tailed random walks
local central limit theorem
potential kernel
stable distributions

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23-EJP996Final published version, 440 KBLicence: CC BY

Cite this

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KW - potential kernel

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Fractional Edgeworth expansions for one-dimensional heavy-tailed random variables and applications

Abstract

Bibliographical note

Funding

Keywords

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