Convergence and stability of an explicit numerical method for stochastic differential equations with piecewise continuous arguments
摘要
Adapted the truncation techniques from Mao (2015) and Li et al. (2019), we propose an explicit numerical method, i.e. the truncated Euler–Maruyama (EM) method for stochastic differential equations with piecewise continuous arguments (SDEPCAs). We establish the strong convergence theory and demonstrate that the convergence rate is 1/2. The mean square exponential stability is investigated. Finally, two numerical experiments are addressed to support the theoretical results.