Three classes of decomposable distributions (Q2053576)

The paper investigates a subclass of positive infinitely divisible random variables \(X\) such that \(cX\mathop = \limits^d {X_c} + {Z_c}\) for any \(c \in (0,1)\), where \(\mathop = \limits^d \) denotes the equality of distributions, \({X_c}\) is the value of a subordinator \(({X_t},t \ge 0)\) at the moment \(t = c\), \({Z_c}\) is a random variable independent of \({X_c}\), and \(X = {X_1}\). It refines some previously obtained results.