Uniform Factorial Decay Estimate for the Remainder of Rough Taylor Expansion

TL;DR

This paper proves a uniform factorial decay estimate for the Taylor expansion remainder of solutions to controlled differential equations, advancing understanding of their approximation behavior.

Contribution

It introduces a novel factorial decay estimate for controlled paths, which underpins the uniform decay estimate for Taylor remainders in rough differential equations.

Findings

Established a factorial decay estimate for controlled paths.

Proved a uniform factorial decay estimate for Taylor remainders.

Enhanced theoretical understanding of rough differential equation approximations.

Abstract

We establish an uniform factorial decay estimate for the Taylor approximation of solutions to controlled differential equations. Its proof requires a factorial decay estimate for controlled paths which is interesting in its own right.