The asymptotic distribution of the scaled remainder for pseudo golden ratio expansions of a continuous random variable

Ira W. Herbst, Jesper Møller, Anne Marie Svane

Let $X=\sum_{k=1}^\infty X_k β^{-k}$ be the base-${\hat{I}}^2$ expansion of a continuous random variable $X$ on the unit interval where ${\hat{I}}^2$ is the positive solution to $β^n = 1 + β+ \cd…