ON R+-WEAKLY STABLE DISTRIBUTION.

A random vector X is called R+-weakly stable if for all (nonnegative) random variables Θ1 and Θ₂ independent of X, X′ there exists a (nonnegative) random variable Θ independent of X such that Θ₁X + Θ₂X′ ^d= ΘX. In this paper, as an answer to the open question given in [J. K. Misiewicz, K. Oleszkiewicz, and K. Urbanik, Studia Math., 167 (2005), pp. 195–213] we show that R+-weakly stable distributions have the same properties and stochastic structure as weakly stable distributions. [ABSTRACT FROM AUTHOR]