Breakdown coefficients of multiplicative cascades having asymmetrically distributed generators with bounded essential range

In previous work [Aguilar Flores et al., Stoch. Environ. Res. Risk Assess. (2021) 35: 1681-1687], distributional convergence of breakdown coefficients (BDCs) to symmetric probability distribution functions of weights in discrete-scale multiplicative cascades has been shown. Asymmetric weights distributions, however, cannot become the limiting functions of symmetric BDC distributions. A procedure has been devised and is presented herein for the computation of the limiting distributions in the aforementioned cases, involving a convolution that is identified with the first-level BDCs probability distribution, and thereby can be used for the purpose of model validation in otherwise non-ergodic single realizations of multiplicative cascade models.