×

zbMATH — the first resource for mathematics

\(L_1\)-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
PDF BibTeX XML Cite
Full Text: DOI