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

Chunmei Shi, Yu Xiao and Chiping Zhang

Abstract and Applied Analysis, 2012, vol. 2012, 1-19

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 ≤ 𠜃 < 1 ) and also contains that of the scale linear SDE, that is, exponential Euler method is analogue mean-square A -stable. Then the exponential stability of the exponential Euler method for scalar semi-linear SDEs is considered. Under the conditions that guarantee the analytic solution is exponentially stable in mean-square sense, the exponential Euler method can reproduce the mean-square exponential stability for any nonzero stepsize. Numerical experiments are given to verify the conclusions.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:350407

DOI: 10.1155/2012/350407

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