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A generalization of the global limit theorems of R. P. Agnew

For distribution functions {Fn,n≥0}, the relationship between the weak convergence of Fn to F0 and the convergence of ∫Rϕ(|Fn−F0|)dx to 0 is studied where ϕ is a nonnegative, nondecreasing function. Sufficient and, separately, necessary conditions are given for the latter convergence thereby general...

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Збережено в:
Автор: Andrew Rosalsky
Формат: Artigo
Мова:Inglês
Опубліковано: Wiley 1988-01-01
Серія:International Journal of Mathematics and Mathematical Sciences
Предмети:
distribution function
global limit theorem
weak convergence
complete convergence
almost everywhere convergence
uniform convergence
sums of independent random variables
central limit theorem
Liapounov condition.
Онлайн доступ:http://dx.doi.org/10.1155/S0161171288000432
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