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Almost Sure and Lp Convergence of Split‐Step Backward Euler Method for Stochastic Delay Differential Equation

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  • Qian Guo
  • Xueyin Tao

Abstract

The convergence of the split‐step backward Euler (SSBE) method applied to stochastic differential equation with variable delay is proven in Lp‐sense. Almost sure convergence is derived from the Lp convergence by Chebyshev’s inequality and the Borel‐Cantelli lemma; meanwhile, the convergence rate is obtained.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:390418
DOI: 10.1155/2014/390418
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