论文标题
颗粒和基于树的奇异FBSDE的融合
Convergence of particles and tree based scheme for singular FBSDEs
论文作者
论文摘要
我们研究了[Chassagneux and Yang，2022]中引入的理论分裂方案的实施，用于单数FBSDE [Carmona and delarue 2013]及其相关的准线性变性PDE。完全可实现的算法基于传输算子和树的粒子近似，例如在理论分裂中出现的扩散算子的近似。在某些合理条件下，我们在系数函数上以数值方法的速率证明了收敛性。这验证了在[Chassagneux and Yang，2022]中获得的一些数值结果。我们以数值部分介绍了算法的各种实现并讨论了它们在实践中的效率。
We study an implementation of the theoretical splitting scheme introduced in [Chassagneux and Yang, 2022] for singular FBSDEs [Carmona and Delarue 2013] and their associated quasi-linear degenerate PDEs. The fully implementable algorithm is based on particles approximation of the transport operator and tree like approximation of the diffusion operator appearing in the theoretical splitting. We prove the convergence with a rate of our numerical method under some reasonable conditions on the coefficients functions. This validates a posteriori some numerical results obtained in [Chassagneux and Yang, 2022]. We conclude the paper with a numerical section presenting various implementations of the algorithm and discussing their efficiency in practice.
