Rough differential equations in the flow approach

We show how the flow approach of Duch, with elementary differentials as coordinates, can be used to prove well-posedness for rough stochastic differential equations driven by fractional Brownian motion with Hurst index $H > \frac{1}{4}$. A novelty appearing here is that we use coordinates for the flow that are indexed by trees rather than multi-indices.

💡 Research Summary

The paper develops a novel framework for solving rough differential equations (RDEs) driven by fractional Brownian motion (fBm) with Hurst index (H>1/4). Building on the “Polchinski flow” introduced by Duch (2021), the authors adapt this renormalisation group (RG) technique to the setting of finite‑dimensional stochastic differential equations of the form
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