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Functional asymptotic confidence intervals for a common mean of independent random variables
Lindeberg's condition symmetric random variable Student statistic Student process Wiener process functional central limit theorem
2009/9/16
We consider independent random variables (r.v.'s) with a common mean $mu$ that either satisfy Lindeberg's condition, or are symmetric around $mu$. Present forms of existing functional central limit th...
The realization of positive random variables via absolutely continuous transformations of measure on Wiener space
positive random variables continuous transformations Wiener space
2009/5/18
Let $mu$ be a Gaussian measure on some measurable space ${W = {w}, calB (W)}$ and let $nu$ be a measure on the same space which is absolutely continuous with respect to $nu$. The paper surveys results...
On exchangeable random variables and the statistics of large graphs and hypergraphs
random variables large graphs large hypergraphs
2009/5/18
In this survey we recall the basic results of the theory of exchangeable laws, and then explain the probabilistic versions of various interesting questions from graph and hypergraph theory that their ...
Strong Laws and Summability for Sequences of $phi$-Mixing Random Variables in Banach Spaces
StrongLaws Summability
2009/5/8
In this note the almost sure convergence of stationary, $varphi$-mixing sequences of random variables with values in real, separable Banach spaces according to summability methods is linked to the ful...
On the strong law of large numbers for d-dimensional arrays of random variables
large numbers d-dimensional arrays random variables
2009/3/31
In this paper, we provide a necessary and sufficient condition for general d-dimensional arrays of random variables to satisfy strong law of large numbers. Then, we apply the result to obtain some str...
Multiplication of free random variables and the S-transform：the case of vanishing mean
free random variable S-transform vanishing mean
2009/3/27
This note extends Voiculescu's S-transform based analytical machinery for free multiplicative convolution to the case where the mean of the probability measures vanishes. We show that with the right i...
Asymptotic results for empirical measures of weighted sums of independent random variables
Asymptotic results empirical measures weighted sums independent random variables
2009/3/27
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...
Multiplication of free random variables and the S-transform: the case of vanishing mean
random variables probability measures S-transform
2009/3/23
This note extends Voiculescu's S-transform based analytical machinery for free multiplicative convolution to the case where the mean of the probability measures vanishes. We show that with the right i...
Asymptotic results for empirical measures of weighted sums of independent random variables
Asymptotic results empirical measures independent random variables
2009/3/23
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...
A note on the invariance principle of the product of sums of random variables
central limit theorem invariance principle random variables
2009/3/23
The central limit theorem for the product of sums of various random variables has been studied in a variety of settings. The purpose of this note is to show that this kind of result is a corollary of ...
Joint Distributions of Waiting Time Random Variables for Patterns
Conditional expectation discrete distribution theory discrete pattern generalized probability generating function waiting time
2009/3/5
Exact joint distributions of waiting times for two patterns in a sequence of l-th order time-homogeneous Markov dependent trials are studied, where the patterns are not necessarily assumed to be disti...
EXTREMAL BEHAVIOUR INMODELS OF SUPERPOSITION OF RANDOM VARIABLES
extreme value nonstationarity extremal index superposition of point processes
2009/2/26
Let X(i) ={Xgi(n)}n1, i=1, 2, be sequences of random variables, where {gi(n)}n1
are disjoint and strictly increasing sequences of integer numbers such that {g1(n)}n1 ∪
{g2(n)}n1 = N. Using super...
ON THE EXCESS DISTRIBUTION OF SUMS OF RANDOM VARIABLES IN BIVARIATEEV MODELS
univariate extreme value distribution multivariate extreme value distribution sums of random variables excess distribution Pickands dependence function linear portfolio risk measure expected shortfall
2009/2/25
We investigate the limit of the excess distribution of aU+ bV in case of an EVD with arbitrary margins and with arbitrary scale parameters a, b > 0. It turns out that the limiting excess df may have a...
Extremes of periodic moving averages of random variables with regularly varying tail probabilities
Periodic moving average processes extremal index mixing condition
2009/2/23
We define a family of local mixing conditions that enable the computation of the extremal index of periodic sequences from the joint distributions of k consecutive variables of the sequence. By applyi...
Functional asymptotic confidence intervals for a common mean of independent random variables
Lindeberg’s condition symmetric random variable Student statistic Student process Wiener process
2010/3/17
We consider independent random variables (r.v.’s) with a common
mean μ that either satisfy Lindeberg’s condition, or are symmetric
around μ. Present forms of existing functional central limit theore...