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2025 Variability and the existence of rough integrals with irregular coefficients
Michael Hinz, Jonas M. Tölle, Lauri Viitasaari
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Electron. Commun. Probab. 30: 1-12 (2025). DOI: 10.1214/25-ECP656

Abstract

Within the context of rough path analysis via fractional calculus, we show how variability can be used to prove the existence of integrals with respect to Hölder continuous multiplicative functionals in the case of Lipschitz coefficients with first order partial derivatives of bounded variation. We discuss applications to certain Gaussian processes, in particular, fractional Brownian motions with Hurst index 13<H12.

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Michael Hinz. Jonas M. Tölle. Lauri Viitasaari. "Variability and the existence of rough integrals with irregular coefficients." Electron. Commun. Probab. 30 1 - 12, 2025. https://doi.org/10.1214/25-ECP656

Information

Received: 10 July 2024; Accepted: 17 January 2025; Published: 2025
First available in Project Euclid: 28 January 2025

arXiv: 2407.06907
Digital Object Identifier: 10.1214/25-ECP656

Subjects:
Primary: 26B30 , 46E35 , 60G15 , 60G17 , 60G22 , 60L20
Secondary: 26A33 , 31B15 , 42B20

Keywords: fractional Brownian motion , fractional rough path integrals , Functions of bounded variation , Gaussian processes , irregular multiplicative functionals , variability

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