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2022 Local and uniform moduli of continuity of chi–square processes
Michael B. Marcus, Jay Rosen
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Electron. Commun. Probab. 27: 1-10 (2022). DOI: 10.1214/22-ECP471

Abstract

Let {ηi(t),t[0,1]}i=1k be independent copies of η={η(t),t[0,1]}, a mean zero continuous Gaussian process. Let

Yk:=Yk(t)=i=1kηi2(t),t[0,1].

This paper shows how exact local (at 0) and uniform moduli of continuity (on [0,1]) of Yk can be obtained from the exact local and uniform moduli of continuity of η.

Funding Statement

Research of Jay Rosen was partially supported by grants from the Simons Foundation.

Citation

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Michael B. Marcus. Jay Rosen. "Local and uniform moduli of continuity of chi–square processes." Electron. Commun. Probab. 27 1 - 10, 2022. https://doi.org/10.1214/22-ECP471

Information

Received: 2 June 2021; Accepted: 20 May 2022; Published: 2022
First available in Project Euclid: 15 June 2022

Digital Object Identifier: 10.1214/22-ECP471

Subjects:
Primary: 60F15 , 60G15 , 60G17

Keywords: chi–square processes , moduli of continuity

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