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On rates of convergence to infinitely divisible laws for dependent random variables
Author(s) -
Basu A. K.
Publication year - 1980
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315235
Subject(s) - mathematics , lipschitz continuity , limit of a function , random variable , limit (mathematics) , law of large numbers , convergence of random variables , convergence (economics) , class (philosophy) , conditional expectation , operator (biology) , value (mathematics) , law , pure mathematics , mathematical analysis , statistics , computer science , biochemistry , chemistry , repressor , artificial intelligence , transcription factor , political science , economics , gene , economic growth
Large O and small o approximations of the expected value of a class of functions (modified K ‐functional and Lipschitz class) of the normalized partial sums of dependent random variables by the expectation of the corresponding functions of infinitely divisible random variables have been established. As a special case, we have obtained rates of convergence to the Stable Limit Laws and to the Weak Laws of Large Numbers. The technique used is the conditional version of the operator method of Trotter and the Taylor expansion.