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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).
Probabilities of moderate deviations for randomly indexed sums of independent and identically dmtributed random variables with multidimensional indices are studied. The results presented extend som...
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
We prove upper estimates for the tail prebabibties: of quadratic and bilinear forms in independent subgaussian randarn vslriabb. These inequalities are used to get upper esthatcs in thc law diterat...
On the rate of convergence to Brownian motion of the partial sums of infima of independent random variables
Let f be a random variable with values in a metric space (X, d). For some class of metric spaces we define in terms of the metric d mathematical expectation of f as a closed bounded and non-empty s...
The problem of cstimating the index of stability and the spectral measure of multivariate stable distribution is related to that of evaluating the risk of stable portfolio of financial assets. We s...
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...

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