伽玛变量Dirichlet和三角形阵列的最大值

Second-order asymptotics on distributions of maxima of bivariate elliptical arrays

Let $\{ (ξ_{ni}, η_{ni}), 1\leq i \leq n, n\geq 1 \}$ be a triangular array of independent bivariate elliptical random vectors with the same distribution function as $(S_{1}, ρ_{n}S_{1}+\sqrt{1-ρ_{n}^2}S_{2})$, $ρ_{n}\in (0,1)$, where $(S_{1},S_{2})$ is a bivariate spherical random vector. For the distribution function of radius $\sqrt{S_{1}^2+S_{2}^2}$ belonging to the max-domain of attraction of the Weibull distribution, Hashorva (2006) derived the limiting distribution of maximum of this triangular array if convergence rate of $ρ_{n}$ to $1$ is given. In this paper, under the refinement of …

非齐次马尔可夫链三角阵列的中心极限定理

Central limit theorem for triangular arrays of Non-Homogeneous Markov chains

本文给出了非齐次马尔可夫链三角形阵列在极大相关系数条件下的中心极限定理。证明是基于鞅技术和一个尖锐的下界估计的方差的部分和。所得结果补充了Dobrushin基于收缩系数的一个重要的中心极限定理。

On the rate of concentration of maxima in Gaussian arrays

Recently in Gao and Stoev (2018) it was established that the concentration of maxima phenomenon is the key to solving the exact sparse support recovery problem in high dimensions. This phenomenon, known also as relative stability, has been little studied in the context of dependence. Here, we obtain bounds on the rate of concentration of maxima in Gaussian triangular arrays. These results are used to establish sufficient conditions for the uniform relative stability of functions of Gaussian arrays, leading to new models that exhibit phase transitions in the exact support recovery problem. Fina…

相依平稳高斯阵列极值的极限律

Limit Laws for Extremes of Dependent Stationary Gaussian Arrays

本文证明了弱相依二元平稳高斯三角阵的分量极大值在归一化为Hüsler-Reiss分布后收敛于分布。在强相依假设下，证明了极大值的极限分布是一个二元高斯分布和Hüsler-Reiss分布的混合分布.我们的论文的另一个发现是，即使在Hüsler和Reiss（1989）的设置中，分量最大值和分量最小值仍然渐近独立，进一步允许弱相关性。在Berman条件下，我们进一步得到了三角阵各分量的几乎必然极限定理。

On the functional CLT for slowly mixing triangular arrays

In \cite{MPU} a functional CLT was obtained for triangular arrays satisfying the Lindeberg condition, that the sum of the individual variances is at most the same order as the variance of the underlying sum, and under the optimal mixing rats $\sum_{n}ρ(2^n)<\infty$, where $ρ(\cdot)$ are the $ρ$-mixing coefficients of the array. In this paper we will present alternative conditions which do not involve the assumption on the sum of variances, and instead we will assume certain maximal moment assumptions (which we can verify for $ϕ$-mixing arrays) and mixing rates of the form $\sum_nρ(e^{G(n)})<\i…

二维离散高斯自由场的极值

Extreme values for two-dimensional discrete Gaussian free field

本文研究了具有Dirichlet边界条件的二维离散高斯自由场的极大值集。我们提供了一个粗略的描述的几何形状的一组附近的最大值，估计两个最大的最大值之间的差距，并估计右尾上的乘法常数的法律中心的最大值。