“…Roughly speaking, non-Gaussian fractional Lévy motions are not self-similar but they belong to a wider class of processes, to the class of dilatively stable processes, which underlines the importance of dilative stability. To put dilative stability into a more general context, we note that there are many other known examples of stochastic processes that do not fit into the scope of self-similarity, but are very natural from the point of view of scaling limit theorems and various types of invariance properties in probability theory, besides Iglói [7], see, e.g., Biermé et al [2], Kaj [9] and Pilipaysjautė and Surgailis [15]. However, there is no common framework for these kinds of processes.…”