Discrete time waveform relaxation method for stochastic delay differential equations (Q618079)

A discrete time waveform relaxation (WR) method is given for numerically approximating the solution of the stochastic delay differential equation \[ dX(t)= f(t,X(t),X(t- \tau))\,dt+ g(t,X(t),X(t-\tau))\, dW(t),\quad t\in(0, T], \] where \(X(t)=\xi(t)\), \(t\in[-\tau,0]\). Mean square convergence of the approximations to the actual solution is proved. Numerical results are provided comparing approximations generated by the WR method to those generated by a semi-implicit Euler method.