Statistics in the p-model

The p-model is a mathematical construction largely applied in physics to construct intermittent distributions on a real interval and in general to study diadic branching processes (cascades). The model produces a hierarchy of Id distributions u((n)) with n = 0, 1, 2..., referred to as generations, that may be used to mimic natural irregular signals at different scales. Here we study the correlation between two p-model generations u((m)) and u((n)) analytically, as well as the skewness and flatness of the values u((n))(x) as depending on the generation indices m and n.