  Dilative semistability extends the notion of semi-selfsimilarity for
infinitely divisible stochastic processes by introducing an additional scaling
in the convolution exponent. It is shown that this scaling relation is a
natural extension of dilative stability and some examples of dilatively
semistable processes are given. We further characterize dilatively stable and
dilatively semistable processes as limits for certain rescaled aggregations of
independent processes.
