Mean-Square Convergence Analysis in the Infinite Time Horizon
摘要
Mean-square convergence is one of the crucial features in assessing the accuracy of stochastic numerical methods. Over the past few decades, considerable attention has been paid to this topic for SFDEs on the finite time horizon. This chapter extends the discussion to the longtime regime. Specifically, we address the following question: for the superlinearly growing coefficients case, how can one obtain the longtime mean-square convergence of numerical methods for the SFDE?