Abstract
In this paper we propose a new numerical method for solving stochastic differential equations (SDEs). As an application of this method we propose an explicit numerical scheme for a super linear SDE for which the usual Euler scheme diverges.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Halidias, N.: Semi-discrete approximations for stochastic differential equations and applications. Int. J. Comput. Math. 780–794 (2012)
Hutzenthaler, M., Jentzen, A., Kloeden, P.E.: Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients. Ann. App. Probab. 22(4), 1611–1641 (2012)
Hutzenthaler, M., Jentzen, A., Kloeden, P.E.: Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients. Proc. R. Soc. A 467(2130), 1563–1576 (2011)
Higham, D., Mao, X., Stuart, A.: Strong convergence of Euler-type methods for nonlinear stochastic differential equations. SIAM J. Numer. Anal. 40, 1041–1063 (2002)
Mao, X., Szpruch, L.: Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients. J. Comput. Appl. Math. 238, 14–28 (2013)
Szpruch, L., Mao, X.: Strong convergence rates for backward Euler-Maruyama method for dissipative-type stochastic differential equations with super-linear diffusion coefficients. Stochastics 85, 144–171 (2013)
Kloeden, P., Platen, E.: Numerical Solution of Stochastic Differential Equations. Springer (1999)
Kloeden, P., Neuenkirch, A.: Convergence of numerical methods for stochastic differential equations in mathematical finance. In: Gerstner, T., Kloeden, P. (eds.) Recent Developments in Computational Finance, pp. 49–80. World Scientific (2013)
Mao, X.: Stochastic Differential Equations and Applications. Horwood Publishing (1997)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Halidias, N. A novel approach to construct numerical methods for stochastic differential equations. Numer Algor 66, 79–87 (2014). https://doi.org/10.1007/s11075-013-9724-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11075-013-9724-9