Stability of a Class of Non-uniform Random Number Generators

It is shown that the asymptotic distribution function modulo 1 of zn+1 = 2azn−bzn, z0 ≠ 0. (a2 − b < 0) does not change under "slight" perturbations of the parameters a and b. More precisely, the asymptotic distribution function of recurrences of this type with non-constant coefficients (a = an, b = bn) is determined.