Improved rectangular method on stochastic Volterra equations (Q629516)

The authors present an improved version of their rectangular method for approximating the solution of the Itô stochastic Volterra integral equation \[ X_t= x+\int^t_0 a(t, X_s)\,ds+ \int^t_0 b(t, X_s)\,dW_s, \] where \(W_t\) is a standard Brownian motion. It is proved that the approximate solutions converge with order \(h\) to the exact solution. Then a modification of the method to facilitate greater ease of computation is introduced and shown to retain the order \(h\) convergence. Numerical results for a simple example are discussed.