I am trying to simulate a multiplicative cascade process. At the first iteration i call four random numbers (between 0 and 1); these numbers are the initial probabilities. In the following step, i call again four random numbers and then multiply them by the parent probabilities as shown in the figure. I repeat the process 6 times. At each iteration, i want the four probabilities (x, y, z, and w) to satisfy the following conditions:
(1) x^2+y^2+z^2+w^2== m, where m is a constant
I have tried to use the "solve" and "vapsolve" tools in matlab, but the problem is that i am getting negative numbers and zero values. I have also tried to set x and y so that i only have two unknowns, but it didn't help.
I will appreciate any help.