Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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STABILITY OF THE MILSTEIN METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS

  • Hu, Lin (Department of Mathematical Sciences and Computing Technology, Central South University) ;
  • Gan, Siqing (Department of Mathematical Sciences and Computing Technology, Central South University)
  • Received : 2010.07.19
  • Accepted : 2010.12.04
  • Published : 2011.09.30
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Abstract

In this paper the Milstein method is proposed to approximate the solution of a linear stochastic differential equation with Poisson-driven jumps. The strong Milstein method and the weak Milstein method are shown to capture the mean square stability of the system. Furthermore using some technique, our result shows that these two kinds of Milstein methods can well reproduce the stochastically asymptotical stability of the system for all sufficiently small time-steps. Some numerical experiments are given to demonstrate the conclusions.

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Acknowledgement

Supported by : The National Natural Science Foundation of China

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