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Numerical Schemes for Stochastic Differential Equations with Variable and Distributed Delays: The Interpolation Approach

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  • Xueyan Zhao
  • Feiqi Deng
  • Shifang Kuang

Abstract

A kind of the Euler‐Maruyama schemes in discrete forms for stochastic differential equations with variable and distributed delays is proposed. The linear interpolation method is applied to deal with the values of the solutions at the delayed instants. The assumptions of this paper on the coefficients and related parameters are somehow weaker than those imposed by the related past literature. The error estimations for the Euler‐Maruyama schemes are given, which are proved to be the same as those for the fundamental Euler‐Maruyama schemes.

Suggested Citation

  • Xueyan Zhao & Feiqi Deng & Shifang Kuang, 2014. "Numerical Schemes for Stochastic Differential Equations with Variable and Distributed Delays: The Interpolation Approach," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:565812
    DOI: 10.1155/2014/565812
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    References listed on IDEAS

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    1. Fischer Paul & Platen Eckhard, 1999. "Applications of the balanced method to stochastic differential equations in filtering," Monte Carlo Methods and Applications, De Gruyter, vol. 5(1), pages 19-38, December.
    2. Eckhard Platen, 1999. "An Introduction to Numerical Methods for Stochastic Differential Equations," Research Paper Series 6, Quantitative Finance Research Centre, University of Technology, Sydney.
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