Weak solutions of rough path SDE's via Girsanov

TL;DR

This paper develops a Girsanov-type theorem for differential equations driven by both Brownian motion and rough paths, enabling the construction of weak solutions in a probabilistic framework.

Contribution

It introduces a Girsanov theorem for rough path driven SDEs, expanding the tools for analyzing such stochastic systems.

Findings

Established a Girsanov transformation for rough path SDEs

Constructed weak solutions using the Girsanov approach

Extended probabilistic methods to rough path driven equations

Abstract

We consider a differential equation driven by a Brownian motion as well as a rough path. We prove a Girsanov-type result for this equation to construct a weak solution in the probabilistic sense.