About atomless random measures on δ-rings

D. Kremer and H.-P. Scheffler

Statistics & Probability Letters, 2020, vol. 164, issue C

Abstract: Independently scattered random measures are usually defined and constructed under the additional condition of being infinitely divisible, a rather strong condition. A more natural condition is the assumption that the random measure has no atoms, that is being atomless. We show that atomless random measures on δ-rings are necessarily infinitely divisible, so infinite divisibility is in fact a quite natural condition.

Keywords: Independently scattered random measures; Atomless random measures; Infinite divisibility; δ-rings; Stochastic integrals (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2020.108805

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