Heuristics for the Probabilistic Solution of BVPs with Mixed Boundary Conditions

Abstract

The performance of stochastic numerical methods for bounded diffusions (accuracy, speed and weak rate of convergence) is considered. The backdrop is the pointwise solution, via stochastic representations, of boundary value problems with mixed boundary conditions. Three stochastic solvers are tested on application-inspired problems, and their performance is noticeably improved thanks to simple heuristics introduced here. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.