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On the Rate of Convergence to a Stable Law
Author(s) -
Hall Peter
Publication year - 1981
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-23.1.179
Subject(s) - mathematics , limit (mathematics) , rate of convergence , law of large numbers , convergence (economics) , central limit theorem , order (exchange) , asymptotic expansion , term (time) , convergence of random variables , random variable , limit of a function , mathematical analysis , statistics , physics , finance , quantum mechanics , economics , economic growth , channel (broadcasting) , electrical engineering , engineering
We obtain rates of convergence and asymptotic expansions in limit theorems for powers of reciprocals of random variables. Our results improve on recent work of Shapiro [ 18 ], who obtained Berry‐Esseen bounds of order n −l/9+ε (ε > 0). Under weaker conditions than Shapiro imposed we obtain asymptotic expansions whose first term is of order n −1 (log n ) 2 .