2017/10/30 by Bruno Bouchard, Bouchard, Bruno, Xiaolu Tan +3
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.48550/arxiv.1710.10933
arxiv created 2017/10/30 · openalex publication_date 2017/10/30 · arxiv updated 2017/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the branching process based numerical algorithm of Bouchard et al. [3], that is dedicated to semilinear PDEs (or BSDEs) with Lipschitz nonlinearity, to the case where the nonlinearity involves the gradient of the solution. As in [3], this requires a localization procedure that uses a priori estimates on the true solution, so as to ensure the well-posedness of the involved Picard iteration scheme, and the global convergence of the algorithm. When, the nonlinearity depends on the gradient, the later needs to be controlled as well. This is done by using a face-lifting procedure. Convergence of our algorithm is proved without any limitation on the time horizon. We also provide numerical simulations to illustrate the performance of the algorithm.