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Strong Approximations of Weighted Sums of Random Variables
Author(s) -
Horváth Lajos
Publication year - 1986
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/s2-33.3.567
Subject(s) - mathematics , law of the iterated logarithm , generalization , logarithm , approximations of π , random variable , limit (mathematics) , iterated logarithm , iterated function , central limit theorem , statistics , mathematical analysis
We develop strong approximations of weighted sums of random variables. The consequences of these approximations are an estimation of the Prohorov‐Lévy distance between weighted partial sums and their limit processes and the functional law of the iterated logarithm. We obtain a generalization of Gaposkin's and Lai's results in the case of Cesàro summability methods.