Bridging rough stochastic differential equations and rough semimartingales

@misc{dause2026bridging,
  title = {{Bridging rough stochastic differential equations and rough semimartingales}},
  author = {Jannis R. Dause and Peter K. Friz and Jost Pieper},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41664},
  eprint = {2610.41664},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41664},
}

TY  - UNPB
TI  - Bridging rough stochastic differential equations and rough semimartingales
AU  - Jannis R. Dause
AU  - Peter K. Friz
AU  - Jost Pieper
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41664
UR  - https://arxiv.org/abs/2610.41664
AB  - We bridge the gap between the mixed-moment theory of càdlàg rough stochastic differential equations (short:RSDEs), introduced by Friz, Hocquet and Lê (2021) and extended to the càdlàg setting by Allan and Pieper (2026), and the theory of rough semimartingales (short:RSMs), introduced by Friz and Zorin-Kranich (2023), by investigating the intersection of these two theories for the first time. By introducing the concept of good solutions to RSDEs, solutions which are simultaneously both mixed-moment solutions and RSMs, we develop a solution concept, which allows for good control on both moment-based and pathwise properties of solutions. The well-posedness of good solutions is proven using a fixed point argument on the space of L^2-martingales by suitably leveraging previously known mixed-moment estimates. Based on these insights we further characterize a large class of good solutions of semi-linear RSDEs through a novel rough stochastic Duhamel's principle.
ER  -