Skip to main content
Log in

Simulation of stochastic differential equations

  • Simalation
  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

A lot of discrete approximation schemes for stochastic differential equations with regard to mean-square sense were proposed. Numerical experiments for these schemes can be seen in some papers, but the efficiency of scheme with respect to its order has not been revealed. We will propose another type of error analysis. Also we will show results of simulation studies carried out for these schemes under our notion.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Gard, T. C. (1988).Introduction to Stochastic Differential Equations, Marcel Dekker, New York.

    Google Scholar 

  • Janssen, R. (1984). Discretization of the Wiener-process in difference-methods for stochastic differential equations,Stochastic Process. Appl.,18, 361–369.

    Google Scholar 

  • Kanagawa, S. (1989). The rate of convergence for approximate solutions of stochastic differential equations,Tokyo J. Math.,12, 33–48.

    Google Scholar 

  • Kloeden, P. E. and Platen, E. (1989). A survey of numerical methods for stochastic differential equations,Stochastic Hydrology and Hydraulics,3, 155–178.

    Google Scholar 

  • Kloeden, P. E. and Platen, E. (1992).Numerical Solution of Stochastic Differential Equations, Springer, Berlin.

    Google Scholar 

  • Liske, H. and Platen, E. (1987). Simulation studies on time discrete diffusion approximations,Math. Comput. Simulation,29, 253–260.

    Google Scholar 

  • Maruyama, G. (1955). Continuous Markov processes and stochastic equations,Rend. Circ. Mat. Palermo,4, 48–90.

    Google Scholar 

  • McShane, E. J. (1974).Stochastic Calculus and Stochastic Models, Academic Press, New York.

    Google Scholar 

  • Mil'shtein, G. N. (1974). Approximate integration of stochastic differential equations,Theory Probab. Appl.,19, 557–562.

    Google Scholar 

  • Newton, N. J. (1991). Asymptotically efficient Runge-Kutta methods for a class of Ito and Stratonovich equations,SIAM J. Appl. Math.,51, 542–567.

    Google Scholar 

  • Pardoux, E. and Talay, D. (1985). Discretization and simulation of stochastic differential equations,Acta Appl. Math.,3, 23–47.

    Google Scholar 

  • Platen, E. (1981). An approximation method for a class of Ito processes,Lithuanian Math. J.,21, 121–133.

    Google Scholar 

  • Rümelin, W. (1982). Numerical treatment of stochastic differential equations,SIAM J. Number. Anal.,19, 604–613.

    Google Scholar 

  • Saito, Y. and Mitsui, T. (1992). Discrete approximations for stochastic differential equations,Transactions of the Japan Society for Industrial and Applied Mathematics,2, 1–16 (in Japanese).

    Google Scholar 

  • Talay, D. (1984). Efficient numerical schemes for the approximation of expectations of functionals of the solution of a SDE and applications,Lectures Notes in Control and Information Sciences,61, Springer, Berlin.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Saito, Y., Mitsui, T. Simulation of stochastic differential equations. Ann Inst Stat Math 45, 419–432 (1993). https://doi.org/10.1007/BF00773344

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00773344

Key words and phrases

Navigation