Vorträge in der Woche 07.09.2026 bis 13.09.2026

Donnerstag, 10.09.2026: An efficient numerical algorithm for backward stochastic PDEs based on the splitting-up method

Juzhou Li

We present an efficient numerical method for solving backward stochastic partial differential equations (BSPDEs), a class of problems notoriously challenging due to the curse of dimensionality because of spatial discretization. Our approach leverages a splitting technique to decompose the original BSPDE into simpler subproblems, effectively alleviates the curse of dimensionality. The optimal first-order strong convergence rate is derived when applied to a general class of non-linear BSPDEs. This convergence rate holds for the solution $u$ itself, and its spatial gradient $\nabla u$, as well as the process $q$. The robustness result is also given. Numerical experiments are also provided to validate the theoretical results.