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Peer-reviewedCC BYBernoulli

Bicausal optimal transport for SDEs with irregular coefficients

  • Michaela Hitz1
  • Benjamin A. Robinson1
  1. 1Department of Statistics, University of Klagenfurt, Klagenfurt, Austria
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Abstract

We solve constrained optimal transport problems in which the marginal laws are given by the laws of solutions of stochastic differential equations (SDEs). We consider SDEs with irregular coefficients, making only minimal regularity assumptions. We show that the so-called synchronous coupling is optimal among bicausal couplings, that is couplings that respect the flow of information encoded in the stochastic processes. Our results provide a method to numerically compute the adapted Wasserstein distance between laws of SDEs with irregular coefficients. We show that this can be applied to quantifying model uncertainty in stochastic optimisation problems. Moreover, we introduce a transformation-based semi-implicit numerical scheme and establish the first strong convergence result for SDEs with exponentially growing and discontinuous drift.

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Cite

BibTeXRIS
BibTeX
@article{hitz2026bicausal,
  title = {{Bicausal optimal transport for SDEs with irregular coefficients}},
  author = {Michaela Hitz and Benjamin A. Robinson},
  journal = {Bernoulli},
  year = {2026},
  month = jul,
  doi = {10.3150/26-bej1985},
  url = {https://doi.org/10.3150/26-bej1985},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Bicausal optimal transport for SDEs with irregular coefficients
AU  - Michaela Hitz
AU  - Benjamin A. Robinson
PY  - 2026
DA  - 2026/07/31
JO  - Bernoulli
DO  - 10.3150/26-bej1985
UR  - https://doi.org/10.3150/26-bej1985
AB  - We solve constrained optimal transport problems in which the marginal laws are given by the laws of solutions of stochastic differential equations (SDEs). We consider SDEs with irregular coefficients, making only minimal regularity assumptions. We show that the so-called synchronous coupling is optimal among bicausal couplings, that is couplings that respect the flow of information encoded in the stochastic processes. Our results provide a method to numerically compute the adapted Wasserstein distance between laws of SDEs with irregular coefficients. We show that this can be applied to quantifying model uncertainty in stochastic optimisation problems. Moreover, we introduce a transformation-based semi-implicit numerical scheme and establish the first strong convergence result for SDEs with exponentially growing and discontinuous drift.
SN  - 1350-7265
SN  - 1573-9759
ER  -