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This note gives the convergence rate in the central limit theorem and the random central limit theorem of some functions of the average of independent random variables.
On the limit behaviour of random sums of independent random variables
Weak convergence of random sums of infima of independent random variables
We give tbe rate of convergence in the central limit theorem and the random central limit theorem for functions belonging to the class I of all real differentiable functions g such that gr E L(1).
The Levy and the Dudley metrics are used to give estimates of the rate convergence in the centrat- limit theorem for some functions of the average of independent random variables.
Topology of the convergence in probability on a linear span of a sequence of independent random variables
Weak convergence to the Brownian motion of the partial sums of infima of independent random variables
On the rate of convergence to Brownian motion of the partial sums of infima of independent random variables
In this paper we present uniform and nonuniform rates of convergence d sums of independent random variables to a stable law. The results obtained extend to the case of nonidentically distributed ra...
Some moment bounds and conditions for sums of independent random variables are considered. In particular, a method is presented to estimate the absolute moments using the related characteristic fun...
We obtain an almost sure convergence limit theorem for independent nonidentically distributed random variablcs. Lct S,, n 2 1, be the partial sums of independent random variables with zero means an...
The purpose of this paper is the proof of an almost sure central limit theorem for subsequences. We obtain an almost sure convergence limit theorem for independent nonidentically distributed random...
We investigate the asymptotic behavior of weighted sums of independent standardized random variables with uniformly bounded third moments. The sequence of weights is given by a family of rectangular m...

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