Volterra equations driven by rough signals. III: Probabilistic construction of the Volterra rough path for fractional Brownian motions

DOI10.1007/s10959-023-01251-yarXiv2202.05076MaRDI QIDQ6204784

Xiao-Hua Wang, Fabian Harang, Samy Tindel

Publication date: 2 April 2024

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.05076

zbMATH Keywords

fractional Brownian motionMalliavin calculussignatureVolterra equationrough path

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07) Rough paths (60L20) Signatures and data streams (60L10)

Cites Work

• The Jain-Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory
• A theory of regularity structures
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• Ramification of rough paths
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• Infinite dimensional pathwise Volterra processes driven by Gaussian noise -- probabilistic properties and applications --
• Geometric versus non-geometric rough paths
• A multiparameter Garsia-Rodemich-Rumsey inequality and some applications
• Multidimensional Stochastic Processes as Rough Paths
• Volatility is rough
• The characteristic function of rough Heston models
• A regularity structure for rough volatility
• A course on rough paths. With an introduction to regularity structures
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