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 $X={\sum }_{k=1}^{\infty }{X}_k{\beta }^{-k}$ be the base-$\beta$ expansion of a continuous random variable $X$ on the unit interval where $\beta$ is the positive solution to $β^n = 1 + β+ \cdots +…