Decomposition of stationary \(\alpha\)-stable random fields. (English) Zbl 1044.60039

Summary: 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.


60G60 Random fields
60G52 Stable stochastic processes
60G57 Random measures
60E07 Infinitely divisible distributions; stable distributions
60G10 Stationary stochastic processes
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