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Original Articles

Double-implicit and split two-step Milstein schemes for stochastic differential equations

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Pages 1987-2011 | Received 01 Feb 2015, Accepted 30 Jul 2015, Published online: 02 Sep 2015
 

Abstract

In this work, we propose two classes of two-step Milstein-type schemes : the double-implicit Milstein scheme and the split two-step Milstein scheme, to solve stochastic differential equations (SDEs). Our results reveal that the two new schemes are strong convergent with order one. Moreover, with a restriction on stepsize, these two schemes can preserve the exponential mean square stability of the original SDEs, and the decay rate of numerical solution will converge to the decay rate of the exact solution. Numerical experiments are performed to confirm our theoretic findings.

2000 AMS Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by NSF of China (Nos. 91130003, 11371157, 1422110, 61473125, and 11301198) and the Fundamental Research Funds for the Central Universities (No. 2013TS137).

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