Non-degeneracy of Stochastic Line Integrals

TL;DR

This paper establishes criteria for the existence of densities of stochastic line integrals driven by fractional Brownian motion and explores the signature uniqueness problem for related rough differential equations.

Contribution

It provides new quantitative criteria for density existence and addresses the signature uniqueness problem in the context of hypoelliptic differential equations driven by fractional Brownian motion.

Findings

Criteria for the existence of densities of stochastic line integrals.

Analysis of signature uniqueness for rough differential equations.

Application to hypoelliptic equations driven by fractional Brownian motion.

Abstract

We derive quantitative criteria for the existence of density for stochastic line integrals and iterated line integrals along solutions of hypoelliptic differential equations driven by fractional Brownian motion. As an application, we also study the signature uniqueness problem for these rough differential equations.