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 1d 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. The behaviour of these quantities is discussed in view of the intermittency characteristics and their applications to physical data analysis are explained briefly.