2018/02/28 by Jean Daniel Mukam, Mukam, Jean Daniel, Antoine Tambue +1
Economics, Econometrics and Finance · #FOS: Mathematics #Financial Risk and Volatility Modeling #Housing Market and Economics #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1803.00423
openalex publication_date 2018/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper aims to investigate the numerical approximation of a general\nsecond order parabolic stochastic partial differential equation(SPDE) driven by\nmultiplicative and additive noise. Our main interest is on such SPDEs where the\nnonlinear part is stronger than the linear part, usually called stochastic\ndominated transport equations. Most standard numerical schemes lose their good\nstability properties on such equations, including the current linear implicit\nEuler method. We discretise the SPDE in space by the finite element method and\npropose a new scheme in time appropriate for such equations, called stochastic\nRosenbrock-Type scheme, which is based on the local linearisation of the\nsemi-discrete problem obtained after space discretisation. We provide a strong\nconvergence of the new fully discrete scheme toward the exact solution for\nmultiplicative and additive noise. Our convergence rates are in agreement with\nresults in the literature. Numerical experiments to sustain our theoretical\nresults are provided.\n