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 $(f_j(\cdot ),{\sigma }^2(\cdot ),{\nu }_j)$, $j=1,2$. The cases $\sigma =0$ and $\sigma >0$ are both treated. We allow ${\nu }_1$ and ${\nu }_2$ to be equivalent time-homogeneous Lévy measures, possibly with infinite variation. Some examples of possible applications are discussed.

9 pages; extended introduction and added references