2024/10/29 by Raffaele D'Ambrosio, Raffaele D’Ambrosio, Stefano Di Giovacchino +2
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Model Reduction and Neural Networks #Numerical methods for differential equations #Stochastic processes and financial applications #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2410.21817
openalex publication_date 2024/10/29 · openalex created_date 2024/11/14 · openalex updated_date 2026/07/28
We address our attention to the numerical time discretization of stochastic Poisson systems via Poisson integrators. The aim of the investigation regards the backward error analysis of such integrators to reveal their ability of being structure-preserving, for long times of integration. In particular, we first provide stochastic modified equations suitable for such integrators and then we rigorously study them to prove accurate estimates on the long-term numerical error along the dynamics generated by stochastic Poisson integrators, with reference to the preservation of the random Hamiltonian conserved along the exact flow of the approximating Wong-Zakai Poisson system. Finally, selected numerical experiments confirm the effectiveness of the theoretical analysis.