Abstract
Let $\{X_k\}_{k \in \mathbb{N}}$ be a nonstationary sequence of random variables. Sufficient conditions are found for the existence of an independent sequence $\{\tilde{X}_k\}_{k \in \mathbb{N}}$ such that $\sup_{x \in \mathbb{R}^1}|P(M_n \leq x) - P(\tilde{M}_n \leq x)| \rightarrow 0$ as $n \rightarrow \infty$, where $M_n$ and $\tilde{M}_n$ are $n$th partial maxima for $\{X_k\}$ and $\{\tilde{X}_k\}$, respectively.
Citation
Adam Jakubowski. "An Asymptotic Independent Representation in Limit Theorems for Maxima of Nonstationary Random Sequences." Ann. Probab. 21 (2) 819 - 830, April, 1993. https://doi.org/10.1214/aop/1176989269
Information