A Truncated Split-Step Forward Euler–Maruyama-Based Method for Stochastic Systems with Non-globally Lipschitz Coefficients

Influenced by Mao (J Comput Appl Math 296:362–375, 2016), we present a truncated split-step forward Euler–Maruyama (TSSFEM) method for stochastic differential equations with non-global Lipschitz coefficients. We study the strong convergence of the new method under local Lipschitz and Khasiminskii conditions. We analyze the mean square stability and asymptotic stability properties of the new method. And finally, we test the advantages of our new findings using various examples. The newly proposed method achieves a strong convergence rate arbitrarily close to half under some additional conditions. We investigate the mean square stability properties of the method based on a scalar linear test equation with multiplicative noise, and the advantages of our results are highlighted by comparing with some well-known methods. We show that the proposed method can preserve the asymptotic stability of the original system under mild conditions. The illustrative examples could successfully demonstrate the improved stability and accuracy of the TSSFEM method.