Exchangeability and infinite divisibility

Abstract

We characterize exchangeability of infinitely divisible distributions in terms of the characteristic triplet. This is applied to stable distributions and selfdecomposable distributions, and a connection to Lévy copulas is made. We further study general mappings between classes of measures that preserve exchangeability and give various examples which arise from discrete time settings, such as stationary distributions of AR(1) processes, or from continuous time settings, such as Ornstein- Uhlenbeck processes or Upsilon-transforms.