On Lévy–Fréchet processes and related self-similar and semi-self-similar ones

Lévy (semi-) stable processes are (semi-) self-similar and, as such, have recently drawn attention of many researchers. On the other hand, there are lots of interesting (semi-) self-similar processes that are not in the Lévy class. Here, we focus on classes of Markov processes related to the extremal processes of Lévy (semi-) stable ones that are all (semi-) self-similar. These are instructive for those working in applied fields.