Electronic Journal of Statistics

Wasserstein and total variation distance between marginals of Lévy processes

Ester Mariucci and Markus Reiß

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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

Creative Commons Attribution 4.0 International License.


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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