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arXiv · 2610.30931

Path-dependent rough differential equations in the full step-two range

Xing Gao·Nannan Li
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Abstract

We establish the existence of solutions to path-dependent rough differential equations with non-anticipative coefficients whose regularity is formulated in terms of horizontal and vertical Dupire derivatives. Under the same regularity assumptions as in Ananova~\cite{An23}, we develop a new causal Taylor argument and establish a second-order remainder estimate. This removes the regularity loss responsible for the restriction $2\leq p<1+\sqrt{2}$ in~\cite{An23} and extends the existence result to the full range $2\le p<3$.

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Xing Gao, Nannan Li. 2026-10-22. Path-dependent rough differential equations in the full step-two range. https://arxiv.org/abs/2610.30931

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