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The Convergence and MS Stability of Exponential Euler Method for Semilinear Stochastic Differential Equations

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  • Chunmei Shi
  • Yu Xiao
  • Chiping Zhang

Abstract

The numerical approximation of exponential Euler method is constructed for semilinear stochastic differential equations (SDEs). The convergence and mean‐square (MS) stability of exponential Euler method are investigated. It is proved that the exponential Euler method is convergent with the strong order 1/2 for semilinear SDEs. A mean‐square linear stability analysis shows that the stability region of exponential Euler method contains that of EM method and stochastic Theta method (0 ≤ θ

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Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:350407
DOI: 10.1155/2012/350407
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