In this paper, we prove the uniqueness of linear i.i.d. representations of non-Gaussian linear processes on a countable abelian group under a basic invertibility condition, without requiring the existence of higher than second moments.
"On the Unique Representation of Non-Gaussian Linear Processes." Ann. Statist. 20 (2) 1143 - 1145, June, 1992. https://doi.org/10.1214/aos/1176348677