Discretization of the Wiener-process in difference-methods for stochastic differential equations

The solution of the stochastic differential equation dx(t) = a(t, x(t)) dt + b(t, x(t)) dw(t), , can be approximated by the Euler-method xn+1 = xn + a(tn,xn) °t + b (tn,xn) °w(tn), if the coefficients are uniformly Lipschitz-continuous. In numerical computations an additional approximation is necessary: the Wiener-process has to be replaced by a suitable simulation. In this paper the effect of this stimulation is analysed and the error estimated in terms of the bounded- Lipschitz-distance for measures on n.