Convergence rate of Euler–Maruyama scheme for stochastic pantograph differential equations

This paper investigates the convergence rate of Euler–Maruyama scheme for a class of stochastic pantograph differential equations, which may not satisfy the general linear growth condition. We reveal that the convergence order for the equations driven by Brownian motion is 1 2 . We also demonstrate that, along with the value of the exponent p ⩾ 2 increasing gradually, the convergence rate for the equations with Markovian jump is decreasing. This conclusion is entirely different from the case without Markovian jump.