The Asymptotic Distribution of the Scaled Remainder for Pseudo Golden Ratio Expansions of a Continuous Random Variable

Let X = ∑ k = 1 ∞ X k β - k be the (greedy) base- β expansion of a continuous random variable X on the unit interval where β is the positive solution to β n = 1 + β + ⋯ + β n - 1 for an integer n ⩾ 2 (i.e., β is a generalization of the golden mean corresponding to n = 2 ). We study the asymptotic di...

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Vydáno v:	Methodology and computing in applied probability Ročník 27; číslo 1; s. 10
Hlavní autoři:	Herbst, Ira W., Møller, Jesper, Svane, Anne Marie
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.03.2025 Springer Nature B.V
Témata:	Asymptotic properties Asymptotic series Business and Management Continuity (mathematics) Economics Electrical Engineering Life Sciences Mathematics and Statistics Random variables Statistics 37A50 60F25 Scaled remainder Asymptotic distribution Pseudo golden mean expansions Invariant distribution 62E17
ISSN:	1387-5841, 1573-7713
On-line přístup:	Získat plný text
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Popis
Shrnutí:	Let X = ∑ k = 1 ∞ X k β - k be the (greedy) base- β expansion of a continuous random variable X on the unit interval where β is the positive solution to β n = 1 + β + ⋯ + β n - 1 for an integer n ⩾ 2 (i.e., β is a generalization of the golden mean corresponding to n = 2 ). We study the asymptotic distribution and convergence rate of the scaled remainder ∑ k = 1 ∞ X m + k β - k when m tends to infinity.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1387-5841 1573-7713
DOI:	10.1007/s11009-025-10137-x