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- W4253804609 abstract "Let {Y n , n ≥ 1} be a sequence of i.i.d. random variables and let l and L denote the essential infimum of Y 1 and the essential supremum of Y 1, respectively. The set ℂ of almost sure limit points of where b > 1 is investigated. The new findings are for the case where Y 1 is unbounded and are as follows: (i) If ℂ ∩ ℝ ≠ ∅, then ℂ = [l, L]; (ii) If l ∈ ℝ, then either ℂ = {∞} or ℂ = [l, ∞]; (iii) If l = − ∞ and L = ∞, then either ℂ = {∞}, ℂ = {− ∞}, ℂ = [− ∞, ∞], or ℂ = {− ∞, ∞}. Illustrative examples are referenced or provided showing that each of the various alternatives can hold. The current work is a continuation of the investigations of Li et al. [3 Li , D. , Qi , Y. , and Rosalsky , A. 2010 . On the set of limit points of normed sums of geometrically weighted i.i.d. bounded random variables . Stochastic Analysis and Applications 28 : 86 – 102 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], 4 Li , D. , Qi , Y. , and Rosalsky , A. 2010 . On the set of limit points of normed sums of geometrically weighted i.i.d. unbounded random variables . Stochastic Analysis and Applications 28 : 862 – 883 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]] wherein the set ℂ is identified, respectively, for bounded Y 1 as the spectrum of the distribution function of and for unbounded Y 1 with 𝔼(log (max {|Y 1|, e})) < ∞ as [l, L]." @default.
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- W4253804609 date "2011-04-20" @default.
- W4253804609 modified "2023-09-28" @default.
- W4253804609 title "On the Set of Limit Points of Normed Sums of Geometrically Weighted I.I.D. Unbounded Random Variables. II" @default.
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- W4253804609 doi "https://doi.org/10.1080/07362994.2011.564449" @default.
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