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PreprintCC0arXiv

Young Parabolic PDEs and the Martingale Problem for Young SDEs

  • Fabio Bugini
  • Michele Coghi
  • Khoa Lê
  • Chengcheng Ling
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Abstract

Under mild regularity assumptions, we prove that the martingale problem associated with the hybrid Young--Lyons--Itô differential equation admits a unique solution in the natural class of solutions satisfying Krylov-type estimates, thereby establishing probabilistic weak well-posedness. Our proof relies on an analysis of the associated Kolmogorov equations, which are Young-type parabolic PDEs with irregular coefficients. The resulting theory for such Young-type parabolic PDEs is also of independent interest.

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Cite

BibTeXRIS
BibTeX
@misc{bugini2026young,
  title = {{Young Parabolic PDEs and the Martingale Problem for Young SDEs}},
  author = {Fabio Bugini and Michele Coghi and Khoa Lê and Chengcheng Ling},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26291},
  eprint = {2610.26291},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26291},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Young Parabolic PDEs and the Martingale Problem for Young SDEs
AU  - Fabio Bugini
AU  - Michele Coghi
AU  - Khoa Lê
AU  - Chengcheng Ling
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26291
UR  - https://arxiv.org/abs/2610.26291
AB  - Under mild regularity assumptions, we prove that the martingale problem associated with the hybrid Young--Lyons--Itô differential equation admits a unique solution in the natural class of solutions satisfying Krylov-type estimates, thereby establishing probabilistic weak well-posedness. Our proof relies on an analysis of the associated Kolmogorov equations, which are Young-type parabolic PDEs with irregular coefficients. The resulting theory for such Young-type parabolic PDEs is also of independent interest.
ER  -