An adaptive time-stepping method based on a posteriori weak error analysis for large SDE systems
In this paper, a numerical scheme based on the semi-implicit Euler method is constructed to approximate solutions of a class of systems of stochastic differential equations. An adaptive mesh strategy (using quasi deterministic rather than random meshes) is developed in which local step size is chosen using an a posteriori weak error estimator. The authors prove convergence with optimal weak order for the estimator and an algorithm for weak adaptive approximation is presented. Then they prove the number of iterations necessary to generate each local step size and the number of time steps needed to cover the desired finite interval. The paper concludes with results of numerical experiments that illustrate advantages of this adaptive strategy over a uniform step size strategy.
scientific article; zbMATH DE number 7437237
scientific article