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

R. Janssen

Stochastic Processes and their Applications, 1984, vol. 18, issue 2, 361-369

Abstract: 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.

Date: 1984
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