The notion of random self-decomposability is generalized here. Its relation to self-decomposability, Harris infinite divisibility and its connection with a stationary first order generalized autoregressive model are presented. The notion is then extended to $\mathbf{Z_+}$-valued distributions.
A further generalization of random self-decomposability
A Generalization and Extension of an Autoregressive Model
On some generalization of the normal distribution
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