Hölder Estimates and Weak Convergences of Certain Weighted Sum Processes

Shigeki Aida () and Nobuaki Naganuma ()
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Shigeki Aida: The University of Tokyo
Nobuaki Naganuma: Kumamoto University

Journal of Theoretical Probability, 2026, vol. 39, issue 1, 1-70

Abstract: Abstract 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.

Keywords: Weighted sum processes; Fourth moment theorem; Malliavin calculus; Rough differential equation; Fractional Brownian motion; Multidimensional Young integral; 60F05; 60H35; 60G15 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10959-025-01456-3

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