L_1-distance for additive processes with time-homogeneous L\'evy measures

TL;DR

This paper derives explicit bounds on the L1-distance between two additive processes with time-homogeneous Lévy measures, covering cases with and without diffusion, and allowing for infinite variation measures.

Contribution

It provides a novel explicit bound for the L1-distance between additive processes with specified local characteristics, including cases with infinite variation Lévy measures.

Findings

Explicit bounds for L1-distance derived

Applicable to processes with infinite variation measures

Handles both diffusive and non-diffusive cases

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 $\sigma > 0$ are both treated. We allow $\nu_1$ and $\nu_2$ to be equivalent time-homogeneous L\'evy measures, possibly with infinite variation. Some examples of possible applications are discussed.