Electronic Journal of Statistics

Wasserstein and total variation distance between marginals of Lévy processes

Ester Mariucci and Markus Reiß

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 12, Number 2 (2018), 2482-2514.

Dates
Received: October 2017
First available in Project Euclid: 27 July 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1532657104

Digital Object Identifier
doi:10.1214/18-EJS1456

Mathematical Reviews number (MathSciNet)
MR3833470

Zentralblatt MATH identifier
06917483

Subjects
Primary: 60G51: Processes with independent increments; Lévy processes 62M99: None of the above, but in this section
Secondary: 60E07: Infinitely divisible distributions; stable distributions

Keywords
Lévy processes Wasserstein distance total variation Toscani-Fourier distance statistical lower bound

Rights
Creative Commons Attribution 4.0 International License.

Citation

Mariucci, Ester; Reiß, Markus. Wasserstein and total variation distance between marginals of Lévy processes. Electron. J. Statist. 12 (2018), no. 2, 2482--2514. doi:10.1214/18-EJS1456. https://projecteuclid.org/euclid.ejs/1532657104


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