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Almost sure convergence and asymptotical normality of a generalization of Kesten's stochastic approximation algorithm for multidimensional case
Kesten's stochastic approximation algorithm multidimensional
2011/6/20
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...
On the almost sure convergence of the square variation of the Brownian motion
the almost sure convergence the square variation the Brownian motion
2009/9/24
On the almost sure convergence of the square variation of the Brownian motion。
On the central limit theorem with almost sure convergence
the central limit theorem almost sure convergence
2009/9/23
On the central limit theorem with almost sure convergence。
On the central limit theorem for independent random variables with almost sure convergence
the central limit theorem independent random variables almost sure convergence
2009/9/22
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...
Almost sure convergence of the distributional limit theorem for order statistics
Almost sure convergence distributional limit theorem order statistics
2009/9/21
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...
A NOTE ON THE ALMOST SURE CONVERGENCE OF CENTRAL ORDER STATISTICS
Central order statistics almost sure limit theorem summation methods
2009/9/18
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...
ON THE RANDOM FUNCTIONAL CENTRAL LIMIT THEOREMS WITH ALMOST SURE CONVERGENCE
Almost sure central limit theorem functional random-sum central limit theorem lbgarithmic averages
2009/9/18
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...
Almost sure convergence of extreme order statistics
almost sure convergence order statistics
2009/9/16
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...