Electronic Communications in Probability

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

Pierre Etoré and Ester Mariucci

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

$L_1$-distance Total Variation Additive Processes

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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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