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The asymptotic distribution of the remainder in a certain base-$\beta$ expansion
- Publication Year :
- 2023
-
Abstract
- 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 $\sum_{k=n+1}^\infty X_k \beta^{n-k}$ when $n$ tends to infinity.<br />Comment: 7 pages
- Subjects :
- Mathematics - Probability
60F25 (Primary) 62E17, 37A50 (Secondary)
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2312.09652
- Document Type :
- Working Paper