WEAK CONVERGENCE OF NONLINEAR TRANSFORMATIONS OF INTEGRATED PROCESSES: THE MULTIVARIATE CASE
WEAK CONVERGENCE OF NONLINEAR TRANSFORMATIONS OF INTEGRATED PROCESSES: THE MULTIVARIATE CASE
复制标题
集成过程非线性变换的弱收敛：多变量情况
作者：
N. Christopeit
研究了满足函数不变性原理的非线性变换随机三角阵列样本均值的弱收敛问题。这种过程的一个基本范例是由综合过程构成的。所获得的结果是最近文献中的工作在多变量和非高斯情况下的推广。作为可容许的非线性变换，引入了一类新的泛函(所谓的局部p-可积函数)，它将Pötscher(2004，计量经济学理论20，1-22)中的局部可积函数的概念应用于多维环境。
We consider weak convergence of sample averages of nonlinearly transformed stochastic triangular arrays satisfying a functional invariance principle. A fundamental paradigm for such processes is constituted by integrated processes. The results obtained are extensions of recent work in the literature to the multivariate and non-Gaussian case. As admissible nonlinear transformation, a new class of functionals (so-called locally p-integrable functions) is introduced that adapts the concept of locally integrable functions in Pötscher (2004, Econometric Theory 20, 1–22) to the multidimensional setting.