Decomposition of stationary $\alpha$-stable random fields

Abstract

This work is concerned with the structural analysis of stationary $\alpha$-stable random fields. Three distinct classes of such random fields are characterized and it is shown that every stationary $\alpha$-stable random field can be uniquely decomposed into the sum of three independent components belonging to these classes. Various examples of stationary $\alpha$-stable random fields are discussed in this context.