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<p>We study weighted sum processes associated with elements in a Wiener chaos with fixed order. More precisely, we show Hölder estimates and a functional limit theorem for them. The main tools we use are the integration by parts formula in Malliavin calculus, the fourth moment theorem, and estimates in multidimensional Young integrals.</p>

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Hölder Estimates and Weak Convergences of Certain Weighted Sum Processes

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月30日

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  • Shigeki Aida,
  • Nobuaki Naganuma

摘要

We study weighted sum processes associated with elements in a Wiener chaos with fixed order. More precisely, we show Hölder estimates and a functional limit theorem for them. The main tools we use are the integration by parts formula in Malliavin calculus, the fourth moment theorem, and estimates in multidimensional Young integrals.