Selfdecomposability and selfsimilarity: a concise primer
Abstract
Description
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 Levy and the additive processes with an emphasis on stationarity and selfsimilarity. Finally we analyze the Ornstein-Uhlenbeck processes driven by Levy noises and their selfdecomposable stationary distributions, and we end with a few particular examples.
24 pages, 3 figures; corrected misprint in the title; redactional modifications required by the referee; added references from [16] to [28];. Accepted and in press on Physica A
24 pages, 3 figures; corrected misprint in the title; redactional modifications required by the referee; added references from [16] to [28];. Accepted and in press on Physica A