Infinitely divisible distribution

Summary

A probability distribution is infinitely divisible if, for every $n$, it is the law of a sum of $n$ independent and identically distributed random variables. The normal, Poisson, gamma and Cauchy laws are infinitely divisible, while no nondegenerate bounded law is. Infinitely divisible laws are exactly the laws at time $1$ of Lévy processes, and they are described by the Lévy–Khintchine representation. They are also the possible limits of sums of many small independent terms.