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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.

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  • 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, Hindawi, vol. 2012, pages 1-24, September.
    • Handle: RePEc:hin:jnlaaa:127397
    DOI: 10.1155/2012/127397
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