Fractional Edgeworth expansions for one-dimensional heavy-tailed random variables and applications
Publication date
2023-08-29
Authors
Chiarini Medeiros, Leandro
Jara, Milton
Ruszel, Wioletta M.
Editors
Advisors
Supervisors
Document Type
Article
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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.
Keywords
discrete stochastic linear stochastic equations, fluctuations, fractional Edgeworth expansion, heavy-tailed random walks, local central limit theorem, potential kernel, stable distributions, Statistics and Probability, Statistics, Probability and Uncertainty
Citation
Chiarini Medeiros, L, Jara, M & Ruszel, W 2023, 'Fractional Edgeworth expansions for one-dimensional heavy-tailed random variables and applications', Electronic Journal of Probability, vol. 28, 108, pp. 1-42. https://doi.org/10.1214/23-EJP996