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It is shown the almost sure convergence and asymptotical normality of a generalization of Kesten's stochastic approximation algorithm for multidimensional case. In this generalization, the step incr...
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...
Let X,, n 2 1, be a sequence of independent and identically distributed rmdom variables and X,,, < X,,, < . . . < X,, denote the order statistics of Xi,.. ., X,. For any sequenoe 01 integers {k,) w...
We prove almost sure versions of distributional limit theorems for central order statistics. We develop a new method which not only gives a simplified proof of existing results in the literature, bu...
In this paper we present functional random-sum central limit theorems with almost sure convergence for independent nonidentically distributed random variables. We consider the case where the summat...
Let $M_{n}^{(k)}$ denote the $k$th largest maximum of a sample $(X_{1},X_{2}, \ldots, X_{n})$ from parent $X$ with continuous distribution. Assume there exist normalizing constants $a_{n}>0$, $b_{n}in...

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