The Lipschitz continuity of the solution to branched rough differential equations

TL;DR

This paper establishes the Lipschitz continuity of solutions to branched rough differential equations using geometric techniques, enhancing understanding of solution stability with respect to initial conditions, vector fields, and driving signals.

Contribution

It introduces a novel application of sub-Riemannian geometry to prove explicit Lipschitz bounds for solutions of branched rough differential equations.

Findings

Explicit Lipschitz continuity with respect to initial data, vector fields, and rough paths

Application of geometric methods to rough differential equations

Enhanced stability analysis of solutions

Abstract

Based on an isomorphism between Grossman Larson Hopf algebra and Tensor Hopf algebra, we apply a sub-Riemannian geometry technique to branched rough differential equations and obtain the explicit Lipschitz continuity of the solution with respect to the initial value, the vector field and the driving rough path.