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$$L_1$$-distance for additive processes with time-homogeneous Lévy measures. (English) Zbl 1300.60017
Summary: 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.

##### MSC:
 60B10 Convergence of probability measures 60E15 Inequalities; stochastic orderings 60G51 Processes with independent increments; Lévy processes
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