Pipiras introduced in the early 2000s an almost surely and uniformly convergent (on compact intervals) wavelet-type expansion of the classical Rosenblatt process. Yet, the issue of estimating, almost surely, its uniform rate of convergence remained an open question. The main goal of our present article is to provide an answer to it in the more general framework of the generalized Rosenblatt process, under the assumption that the underlying wavelet basis belongs to the class due to Meyer. The main ingredient of our strategy consists in expressing in a non-classical (new) way the approximation errors related with the approximation spaces of a multiresolution analysis of \(L^2({{\mathbb {R}}}^2)\). Such a non-classical expression may also be of interest in its own right.

中文翻译：

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广义Rosenblatt过程的小波类型展开及其收敛速度

Pipiras在2000年代初期引入了经典Rosenblatt过程的几乎确定且均匀收敛的（小区间）小波型扩展。但是，几乎可以肯定地估计其统一收敛速度的问题仍然是一个悬而未决的问题。本文的主要目的是在广义的Rosenblatt过程的更一般框架中提供一个答案，并假设基础小波基础属于Meyer所归类。我们策略的主要组成部分在于以非经典（新）方式表示与\（L ^ 2（{{\\ mathbb {R}}} ^ 2）\的多分辨率分析的逼近空间有关的逼近误差。 ）。这样的非古典表达本身也可能引起人们的兴趣。