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Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii‐Type Conditions

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  • Minghui Song
  • Hui Yu

Abstract

The Euler method is introduced for stochastic differential delay equations (SDDEs) with Poisson random measure under the generalized Khasminskii‐type conditions which cover more classes of such equations than before. The main aims of this paper are to prove the existence of global solutions to such equations and then to investigate the convergence of the Euler method in probability under the generalized Khasminskii‐type conditions. Numerical example is given to indicate our results.

Suggested Citation

  • Minghui Song & Hui Yu, 2012. "Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii‐Type Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:127397
    DOI: 10.1155/2012/127397
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    References listed on IDEAS

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    1. Nicola Bruti-Liberati & Eckhard Platen, 2007. "Approximation of jump diffusions in finance and economics," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 283-312, May.
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    3. NicolaBruti-Liberati & Eckhard Platen, 2007. "Strong approximations of stochastic differential equations with jumps," Published Paper Series 2007-7, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    4. Nicola Bruti-Liberati & Eckhard Platen, 2005. "On the Strong Approximation of Jump-Diffusion Processes," Research Paper Series 157, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Cited by:

    1. Shifang Kuang & Yunjian Peng & Feiqi Deng & Wenhua Gao, 2013. "Exponential Stability and Numerical Methods of Stochastic Recurrent Neural Networks with Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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