Selfdecomposability and selfsimilarity: A concise primer

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