Selfdecomposability and selfsimilarity: a concise primer

We summarize the relations among three classes of laws: infinitely divisible, self-decomposable and stable. First we look at them as the solutions of the Central Limit Problem; then their role is scrutinized in relation to the Levy and the additive processes with an emphasis on stationarity and self-similarity. Finally we analyze the Ornstein–Uhlenbeck processes driven by Levy noises and their self-decomposable stationary distributions, and we end with a few particular examples