Electronic Communications in Probability

$L_1$-distance for additive processes with time-homogeneous Lévy measures

Pierre Etoré and Ester Mariucci

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Abstract

We give an explicit bound for the $L_1$-distance between two additive processes of local characteristics $(f_j(\cdot),\sigma^2(\cdot),\nu_j)$, $j = 1,2$. The cases $\sigma =0$ and $\sigma(\cdot) > 0$ are both treated. We allow $\nu_1$ and $\nu_2$ to be time-homogeneous Lévy measures, possibly with infinite variation. Some examples of possible applications are discussed.<br /><br />

Article information

Source
Electron. Commun. Probab., Volume 19 (2014), paper no. 57, 10 pp.

Dates
Accepted: 21 August 2014
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465316759

Digital Object Identifier
doi:10.1214/ECP.v19-3678

Mathematical Reviews number (MathSciNet)
MR3254736

Zentralblatt MATH identifier
1300.60017

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 60E15 60G51: Processes with independent increments; Lévy processes

Keywords
$L_1$-distance Total Variation Additive Processes

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Etoré, Pierre; Mariucci, Ester. $L_1$-distance for additive processes with time-homogeneous Lévy measures. Electron. Commun. Probab. 19 (2014), paper no. 57, 10 pp. doi:10.1214/ECP.v19-3678. https://projecteuclid.org/euclid.ecp/1465316759


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