Informal Introduction Let V be a vector space, and suppose is a stochastic process ranging over V .
Imagine as describing the random jigglings of some particle moving in space. Suppose that the jiggling of the particle results from a succession of independent perturbations occuring over time. We assume that these perturbations all occur independently of one another, and we assume that, as random variables, they are all identically distributed. In other words, for fixed , the random variable can be written as sum of an arbitrarily large number of independent, identically distributed random variables. A random variable of this type is called infinitely divisible.