Existence conditions of permanental distributions are deeply connected to existence conditions of multivariate negative binomial distributions. The aim of this paper is twofold. It answers several questions generated by recent works on this subject, but it also goes back to the roots of this field and fixes existing gaps in older papers concerning conditions of infinite divisibility for these distributions.
"Existence conditions of permanental and multivariate negative binomial distributions." Ann. Probab. 45 (6B) 4786 - 4820, November 2017. https://doi.org/10.1214/17-AOP1179