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

We give an explicit bound for the $L_1$-distance between two additive processes of local characteristics $(f_j(\cdot ),{\sigma }^2(\cdot ),{\nu }_j)$, $j = 1,2$\mathrm{.}Thecases$\sigma =0$and$\sigma > 0$arebothtreated\mathrm{.}Weallow$\nu_1$and$\nu_2$ to be equivalent time-homogeneous L'evy measures, possibly with infinite variation. Some examples of possible applications are discussed.