Selfdecomposability and selfsimilarity: a concise primer

Details Selfdecomposability and selfsimilarity: a concise primer Selfdecomposability and selfsimilarity: a concise primer

2007-08-09

arxiv.org/abs/0708.1239v3

Physica A 387 (2008) 1875-94

Physics

Condensed Matter

Statistical Mechanics

24 pages, 3 figures; corrected misprint in the title; redactional modifications required by the referee; added references from

Scientific paper

10.1016/j.physa.2007.11.036

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.

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