The convergence of truncated euler-maruyama method for stochastic differential equations with piecewise continuous arguments under generalized one-sided lipschitz condition

In this paper, we consider the stochastic differential equations with piecewise continu-ous arguments (SDEPCAs) in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition. Since the delay term t - [t] of SDEPCAs is not continuous and differentiable, the variable sub-stitution method is not suitable. To overcome this difficulty, we adopt new techniques to prove the boundedness of the exact solution and the numerical solution. It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of Lq over bar (q over bar & GE; 2). We obtain the convergence order with some additional conditions. An example is presented to illustrate the analytical theory.