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...

We prove some heavy-traffic limit theorems for processes which encompass the fractionally integrated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a non-Gaussian stable distribution.