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2018 Wasserstein and total variation distance between marginals of Lévy processes
Ester Mariucci, Markus Reiß
Electron. J. Statist. 12(2): 2482-2514 (2018). DOI: 10.1214/18-EJS1456

Abstract

We present upper bounds for the Wasserstein distance of order $p$ between the marginals of Lévy processes, including Gaussian approximations for jumps of infinite activity. Using the convolution structure, we further derive upper bounds for the total variation distance between the marginals of Lévy processes. Connections to other metrics like Zolotarev and Toscani-Fourier distances are established. The theory is illustrated by concrete examples and an application to statistical lower bounds.

Citation

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Ester Mariucci. Markus Reiß. "Wasserstein and total variation distance between marginals of Lévy processes." Electron. J. Statist. 12 (2) 2482 - 2514, 2018. https://doi.org/10.1214/18-EJS1456

Information

Received: 1 October 2017; Published: 2018
First available in Project Euclid: 27 July 2018

zbMATH: 06917483
MathSciNet: MR3833470
Digital Object Identifier: 10.1214/18-EJS1456

Subjects:
Primary: 60G51, 62M99
Secondary: 60E07

JOURNAL ARTICLE
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Vol.12 • No. 2 • 2018
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