Bicausal optimal transport for SDEs with irregular coefficients
arXiv:2403.09941 · doi:10.3150/26-BEJ1985
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.
44 pages, 5 figures
References in corpus (15)
- Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
- Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
- A note on tamed Euler approximations
- A Strong Order 1/2 Method for Multidimensional SDEs with Discontinuous Drift
- Solving high-dimensional optimal stopping problems using deep learning
- A Numerical Method for SDEs with Discontinuous Drift
- Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient
- All Adapted Topologies are Equal
- An adaptive Euler-Maruyama scheme for stochastic differential equations with discontinuous drift and its convergence analysis
- On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift
- The Euler-Maruyama Scheme for SDEs with Irregular Drift: Convergence Rates via Reduction to a Quadrature Problem
- Quantifying a convergence theorem of Gyöngy and Krylov
- Existence and uniqueness of solutions of SDEs with discontinuous drift and finite activity jumps
- On the Existence of Solutions of a Class of SDEs with Discontinuous Drift and Singular Diffusion
- Adapted Wasserstein distance between the laws of SDEs