Asymptotics of One-Dimensional Lévy Approximations

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Asymptotics of One-Dimensional Lévy Approximations. / Berger, Arno; Xu, Chuang.

In: Journal of Theoretical Probability, Vol. 33, No. 2, 2020, p. 1164-1195.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Berger, A & Xu, C 2020, 'Asymptotics of One-Dimensional Lévy Approximations', Journal of Theoretical Probability, vol. 33, no. 2, pp. 1164-1195. https://doi.org/10.1007/s10959-019-00893-1

APA

Berger, A., & Xu, C. (2020). Asymptotics of One-Dimensional Lévy Approximations. Journal of Theoretical Probability, 33(2), 1164-1195. https://doi.org/10.1007/s10959-019-00893-1

Vancouver

Berger A, Xu C. Asymptotics of One-Dimensional Lévy Approximations. Journal of Theoretical Probability. 2020;33(2):1164-1195. https://doi.org/10.1007/s10959-019-00893-1

Author

Berger, Arno ; Xu, Chuang. / Asymptotics of One-Dimensional Lévy Approximations. In: Journal of Theoretical Probability. 2020 ; Vol. 33, No. 2. pp. 1164-1195.

Bibtex

@article{f18a29209ff1437abedcf5430434402e,
title = "Asymptotics of One-Dimensional L{\'e}vy Approximations",
abstract = "For arbitrary Borel probability measures on the real line, necessary and sufficient conditions are presented that characterize best purely atomic approximations relative to the classical L{\'e}vy probability metric, given any number of atoms, and allowing for additional constraints regarding locations or weights of atoms. The precise asymptotics (as the number of atoms goes to infinity) of the approximation error is identified for the important special cases of best uniform (i.e. all atoms having equal weight) and best (i.e. unconstrained) approximations, respectively. When compared to similar results known for other probability metrics, the results for L{\'e}vy approximations are more complete and require fewer assumptions.",
keywords = "Approximation error, Asymptotic point distribution, Best (uniform) approximation, Inverse function, Inverse measure, L{\'e}vy probability metric",
author = "Arno Berger and Chuang Xu",
year = "2020",
doi = "10.1007/s10959-019-00893-1",
language = "English",
volume = "33",
pages = "1164--1195",
journal = "Journal of Theoretical Probability",
issn = "0894-9840",
publisher = "Springer",
number = "2",

}

RIS

TY - JOUR

T1 - Asymptotics of One-Dimensional Lévy Approximations

AU - Berger, Arno

AU - Xu, Chuang

PY - 2020

Y1 - 2020

N2 - For arbitrary Borel probability measures on the real line, necessary and sufficient conditions are presented that characterize best purely atomic approximations relative to the classical Lévy probability metric, given any number of atoms, and allowing for additional constraints regarding locations or weights of atoms. The precise asymptotics (as the number of atoms goes to infinity) of the approximation error is identified for the important special cases of best uniform (i.e. all atoms having equal weight) and best (i.e. unconstrained) approximations, respectively. When compared to similar results known for other probability metrics, the results for Lévy approximations are more complete and require fewer assumptions.

AB - For arbitrary Borel probability measures on the real line, necessary and sufficient conditions are presented that characterize best purely atomic approximations relative to the classical Lévy probability metric, given any number of atoms, and allowing for additional constraints regarding locations or weights of atoms. The precise asymptotics (as the number of atoms goes to infinity) of the approximation error is identified for the important special cases of best uniform (i.e. all atoms having equal weight) and best (i.e. unconstrained) approximations, respectively. When compared to similar results known for other probability metrics, the results for Lévy approximations are more complete and require fewer assumptions.

KW - Approximation error

KW - Asymptotic point distribution

KW - Best (uniform) approximation

KW - Inverse function

KW - Inverse measure

KW - Lévy probability metric

UR - http://www.scopus.com/inward/record.url?scp=85064280387&partnerID=8YFLogxK

U2 - 10.1007/s10959-019-00893-1

DO - 10.1007/s10959-019-00893-1

M3 - Journal article

AN - SCOPUS:85064280387

VL - 33

SP - 1164

EP - 1195

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

SN - 0894-9840

IS - 2

ER -

ID: 223822031