New Math Paper Explores Universal Approximation with Brownian Signatures

A new paper introduces $L^p$-universal approximation theorems for functionals on rough path spaces, demonstrating that linear functionals on signatures of time-extended rough paths can approximate any $p$-integrable stochastic process. This work extends to Gaussian processes, including fractional Brownian motion, and has implications for approximating solutions to stochastic differential equations. The research was submitted to arXiv on December 18, 2025, with a revised version on July 6, 2026. AI

IMPACT This research could advance the theoretical underpinnings for AI models dealing with sequential or time-series data by providing new approximation capabilities.

RANK_REASON The cluster contains a single academic paper published on arXiv. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

• arXiv
• Brownian signatures
• Fractional Brownian motion
• Gaussian Processes
• Mihriban Ceylan
• Stochastic Differential Equations

• paper
• other

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