Unifying and generalizing previous investigations for vector spaces and for locally compact groups, E. Siebert obtained the following remarkable result: A Lévy process on a completely metrizable topological group G, resp. a continuous convolution semigroup (µt)t≥0 of probabilities, satisfies a moment condition ∫ ƒdµt < ∞ for some submultiplicative function ƒ > 0 if and only if the jump measure of the process, ∫resp. the Lévy measure η of the continuous convolution semigroup, satisfies ∫CUƒdη < ∞ for some neighbourhood U of the unit e. Here we generalize this result to additive processes, resp. convolution hemigroups (µs,t)s≤t on (second countable) locally compact groups.
2000 AMS Mathematics Subject Classification: Primary: 60B15; Secondary: 60G51, 43A05, 47D06.