Convergence Rate of Numerical Solutions for Nonlinear Stochastic Pantograph Equations with Markovian Switching and Jumps - Zhenyu Lu; Tingya Yang; Yanhan Hu; Junhao Hu (Abstract and Applied Analysis)
The sufficient conditions of existence and uniqueness of the solutions for nonlinear stochastic pantograph equations with Markovian switching and jumps are given. It is proved that Euler-Maruyama scheme for nonlinear stochastic pantograph equations with Markovian switching and Brownian motion is of convergence with strong order 1/2. For nonlinear stochastic pantograph equations with Markovian switching and pure jumps, it is best to use the mean-square convergence, and the order of mean-square convergence is close to 1/2.