On the L\'evy-Khinchin decomposition of generating functionals
Uwe Franz, Malte Gerhold, Andreas Thom
TL;DR
This paper investigates the conditions under which generating functionals can be decomposed via the Lévy-Khinchin formula, revealing that such decompositions are not always possible and that the conditions are not equivalent.
Contribution
It provides a detailed analysis of various sufficient conditions for Lévy-Khinchin decompositions and demonstrates their non-equivalence and limitations.
Findings
Not all generating functionals admit a Lévy-Khinchin decomposition.
Different sufficient conditions are not equivalent.
Decomposition existence is not guaranteed in general.
Abstract
We study several sufficient conditions for the existence of a L\'evy-Khinchin decomposition of generating functionals. We show that none of these conditions are equivalent and we show that such a decomposition does not always exist.
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