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pro vyhledávání: '"60F25 (Primary) 62E17, 37A50 (Secondary)"'
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 $\beta^n = 1 + \beta + \cdots + \beta^{n-1}$ for an integer $n\ge 2$ (i.e., $\be
Externí odkaz:
http://arxiv.org/abs/2404.08387
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 golden ratio. We study the asymptotic distribution and convergence rate of the scaled remainder $\sum
Externí odkaz:
http://arxiv.org/abs/2312.09652
Let $X_1,X_2,...$ be the digits in the base-$q$ expansion of a random variable $X$ defined on $[0,1)$ where $q\ge2$ is an integer. For $n=1,2,...$, we study the probability distribution $P_n$ of the (scaled) remainder $T^n(X)=\sum_{k=n+1}^\infty X_k
Externí odkaz:
http://arxiv.org/abs/2307.06685