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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≤ p<1+√2 in~\cite{An23} and extends the existence result to the full range 2≤ p<3.

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Cite

BibTeXRIS
BibTeX
@misc{gao2026pathdependent,
  title = {{Path-dependent rough differential equations in the full step-two range}},
  author = {Xing Gao and Nannan Li},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30931},
  eprint = {2610.30931},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30931},
}
RIS
TY  - UNPB
TI  - Path-dependent rough differential equations in the full step-two range
AU  - Xing Gao
AU  - Nannan Li
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.30931
UR  - https://arxiv.org/abs/2610.30931
AB  - 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≤ p<1+√2 in~\cite{An23} and extends the existence result to the full range 2≤ p<3.
ER  -