# Convergence of the Deep BSDE method for FBSDEs with non-Lipschitz coefficients

arXiv: https://arxiv.org/abs/2101.01869 · HTML: https://mlsanity.com/paper/2101.01869/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jan 2021.

## Built on by (most cited first, 7 of 7)

- [Solving high-dimensional parabolic PDEs using the tensor train format](https://mlsanity.com/paper/2102.11830/) (2021)
- [Convergence of a robust deep FBSDE method for stochastic control](https://mlsanity.com/paper/2201.06854/) (2022)
- [From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEs](https://mlsanity.com/paper/2307.15496/) (2023)
- [A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations](https://mlsanity.com/paper/2404.08456/) (2024)
- [Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations](https://mlsanity.com/paper/2310.03393/) (2023)
- [Deep Generative Modeling with Backward Stochastic Differential Equations](https://mlsanity.com/paper/2304.04049/) (2023)
- [Error analysis for the deep Kolmogorov method](https://mlsanity.com/paper/2508.17167/) (2025)

## Abstract (arXiv)

This paper is dedicated to solving high-dimensional coupled FBSDEs with non-Lipschitz diffusion coefficients numerically. Under mild conditions, we provided a posterior estimate of the numerical solution that holds for any time duration. This posterior estimate validates the convergence of the recently proposed Deep BSDE method. In addition, we developed a numerical scheme based on the Deep BSDE method and presented numerical examples in financial markets to demonstrate the high performance.