Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

Universal approximation with signatures of non-geometric rough paths

We establish a universal approximation theorem for signatures of rough paths that are not necessarily weakly geometric. By extending the path with time and its rough path bracket terms, we prove that linear functionals of the signature of the resulting rough paths approximate continuous functionals

Lab Rats Math 8.5 Rigor 4.5 ·  February 5, 2026

Pathwise analysis of log-optimal portfolios

Based on the theory of càdlàg rough paths, we develop a pathwise approach to analyze stability and approximation properties of portfolios along individual price trajectories generated by standard models of financial markets. As a prototypical example from portfolio theory, we study the log-optimal p

Lab Rats Math 9.5 Rigor 1.5 ·  July 24, 2025

Universal approximation property of neural stochastic differential equations

We identify various classes of neural networks that are able to approximate continuous functions locally uniformly subject to fixed global linear growth constraints. For such neural networks the associated neural stochastic differential equations can approximate general stochastic differential equat

Lab Rats Math 8.5 Rigor 1.5 ·  March 20, 2025

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