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

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  • Janssen, R.

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.

Suggested Citation

  • Janssen, R., 1984. "Discretization of the Wiener-process in difference-methods for stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 18(2), pages 361-369, November.
    • Handle: RePEc:eee:spapps:v:18:y:1984:i:2:p:361-369
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    Cited by:

    1. Yoshihiro Saito & Taketomo Mitsui, 1993. "Simulation of stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 419-432, September.

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