Central limit theoremBogoliubov transformationsWe consider the time evolution of N bosons in the mean field regime for factorized initial data. In the limit of large N , the many body evolution can be approximated by the non-linear Hartree equation. In this paper we are interested in the ...
Martingale theory is used to obtain a central limit theorem for degenerate U-statistics with variable kernels, which is applied to derive central limit theorems for the integrated square error of multivariate nonparametric density estimators. Previous approaches to this problem have employed Komlós-Major...
高斯分布的另一种情况是当考虑多个随机变量的和时。由中心极限定理(central limit theorem (due to Laplace))知,在一定的温和条件下(certain mild conditions),一组随机变量的和,当然它本身就是一个随机变量,它的分布随着项数的增加而逐渐趋于高斯分布(Walker, 1969)。 这一点可以考虑N个变量 ,每个变量在[0,1]...
Functional limit theorems for power series with rapid decay of moving averages of Hermite processes Furthermore, we prove convergence in the multivariate case with both, short- and long-range dependent components. Applying this theorem, we obtain a ... JR Gehringer - 《Stochastics & Dynamics》 ...
Its importance derives mainly from the multivariate central limit theorem. The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly) correlated real-valued random variables each of which clusters around a mean value. http://www.chinacloud.cn/show...
We address the question of a Berry-Esseen type theorem for the speed of convergence in a multivariate free central limit theorem. For this, we estimate the difference between the operator-valued Cauchy transforms of the normalized partial sums in an operator-valued free central limit theorem and ...
The convergence of 1 S tof (Y , (s), ) g ( (s) | Y , ) L( ; Y ) can be justified by the central limit theorem, though it requires the variance of f (Y , (s), ) g ( (s) | Y , ) to be finite. Koopman and Shephard (2004) proposed a test to check the validity ...
This paper addresses the key challenge of estimating the asymptotic covariance associated with the Markov chain central limit theorem, which is essential for visualizing and terminating Markov Chain Monte Carlo (MCMC) simulations. We focus on summarizing batching, spectral, and initial sequence covariance...
The Multivariate Central Limit TheoremCovariance and CorrelationCovariance Matrices and Some ApplicationsThe Multivariate Normal ... VI Rotar - 《Crc Press》 被引量: 3发表: 2012年 How Uncertain is the Survival Extrapolation? A Study of the Impact of Different Parametric Survival Models on Extrapolated...
and Proposition 5 of Lesson 2 guarantees that it is linear if f is a (p+1)-dimensional normal density. Even if our random variables do not have a multivariate normal distribution (which is very usual by the Multivariate Central Limit Theorem), a linear approximation makes sense. Frequently,...