Heavy Tails

Abstract

When we talk about the “tails” of a one-dimensional random variable X, we usually think about probabilities of the type P(X > x) and P(X < −x) for a large positive x, with the appropriate meaning of “right tail” and “left tail.” If (X(t),t∈ℝ) or (Xn,n∈ℤ) is a stationary stochastic process, the kind of marginal tails the process has may significantly impact the way memory expresses itself in the process. Particularly important is the distinction between stochastic processes with “light tails” and those with “heavy tails.”.