2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64824We study perpetuities of a special type related to the size-biased distributions. Necessary and sufficient conditions of their existence and uniqueness are obtained. A crucial point in proving all results is a close connection between perpetuities treated in the paper and fixed points of so-called Poisson shot noise transforms.10 pages, Proceedings paperProbabilityPrimary 60E07; Secondary 60K05text