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

Abstract

We give an explicit bound for the $L_1$-distance between two additive processes of local characteristics $(f_j(\cdot),σ^2(\cdot),ν_j)$, $j = 1,2$. The cases $σ=0$ and $σ> 0$ are both treated. We allow $ν_1$ and $ν_2$ to be equivalent time-homogeneous Lévy measures, possibly with infinite variation. Some examples of possible applications are discussed.

9 pages; extended introduction and added references