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Precise Asymptotics in the Baum–Katz and Davis Laws of Large Numbers ofp-mixing Sequences

✍ Scribed by Wei Huang; Ye Jiang; Li Xin Zhang

Book ID
106277644
Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Year
2005
Tongue
English
Weight
227 KB
Volume
21
Category
Article
ISSN
1439-7617

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Precise Asymptotics in the Baum–Katz and
Precise Asymptotics in the Baum–Katz and Davis Laws of Large Numbers
✍ Allan Gut; Aurel Spătaru 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 109 KB

of i.i.d. random variables such that EX s 0, let 1 2 Z be a random variable possessing a stable distribution G with exponent ␣, 1 -␣ F 2, assume the distribution of X is attracted to G, and set S s X n 1 q иии qX . We prove that n p Ž ␣ p rŽ ␣yp..Ž r r py1. r r py2 1 r p yŽ ␣ p rŽ ␣yp..Ž r r py1.