General model of subtraction of stochastic variables. Attractor and stability analysis

We introduce a general process designed to model stochastic systems in which the dependence of random variables is not through addition only but combined addition and subtraction with bounded ranges, and whose probabilistic factors have compact support. We show that, still retaining much of the general essence of the Central Limit Theorem, this process presents a functional attractor which is neither Gaussian nor Lévy like, and is precisely akin numerically to a probability density function shown in previous works to have ubiquitous character, namely the two-parameter beta distribution.