Infinite divisibility (probability, $\mu ={\mu }_n^{\ast n}\text{for every }n\ge 1$)

A probability distribution is infinitely divisible if, for every positive integer $n$, it is the distribution of a sum of $n$ independent and identically distributed random variables. Their common distribution may depend on $n$. A normal distribution has this property by dividing its mean and variance by $n$; a Poisson distribution has it by dividing its rate. The unit-time law of a Lévy process is infinitely divisible because it is the sum of its increments on $n$ equal time intervals.