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Stability, discretization, and optimality of continuous-time causal optimal transport

  • Yifan Jiang
  • Fang Rui Lim
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Abstract

We prove stability of continuous-time causal and bicausal optimal transport problems when both marginals converge in adapted Wasserstein distance along common vanishing time shifts. The marginal laws, filtrations, and costs may all vary, while the limit remains the original causal or bicausal transport problem. This allows for time discretization and the approximation of transport problems between non-degenerate scalar fractional stochastic differential equations by their Wong--Zakai schemes. We further establish sufficient conditions so that the synchronous coupling is optimal for the bicausal transport problem between scalar fractional stochastic differential equations under continuous, nonnegative submodular costs of polynomial growth. This result covers all Hurst parameters H∈(0,1) up to an additional order-preserving commutator condition on the corresponding coefficients for the rough regime H∈(0,1/2).

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Cite

BibTeXRIS
BibTeX
@misc{jiang2026stability,
  title = {{Stability, discretization, and optimality of continuous-time causal optimal transport}},
  author = {Yifan Jiang and Fang Rui Lim},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00353},
  eprint = {2611.00353},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00353},
}
RIS
TY  - UNPB
TI  - Stability, discretization, and optimality of continuous-time causal optimal transport
AU  - Yifan Jiang
AU  - Fang Rui Lim
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00353
UR  - https://arxiv.org/abs/2611.00353
AB  - We prove stability of continuous-time causal and bicausal optimal transport problems when both marginals converge in adapted Wasserstein distance along common vanishing time shifts. The marginal laws, filtrations, and costs may all vary, while the limit remains the original causal or bicausal transport problem. This allows for time discretization and the approximation of transport problems between non-degenerate scalar fractional stochastic differential equations by their Wong--Zakai schemes. We further establish sufficient conditions so that the synchronous coupling is optimal for the bicausal transport problem between scalar fractional stochastic differential equations under continuous, nonnegative submodular costs of polynomial growth. This result covers all Hurst parameters H∈(0,1) up to an additional order-preserving commutator condition on the corresponding coefficients for the rough regime H∈(0,1/2).
ER  -