The Effects of θ on Stability in the θ-Milstein Method for Stochastic Differential Equations
The Effects of θ on Stability in the θ-Milstein Method for Stochastic Differential Equations
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发表时间：
2022
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通讯作者：
Chen Lin
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作者：
Meng Xuejing;Chen Lin
We consider the mean square stability of the θ-Milstein method for stochastic differential equations with local Lipschitz continuous coefficients. For θ ∈ [0, 1=2), a counter example shows that the θ-Milstein method cannot reproduce the stability of the exact solution. By slightly strengthening the local Lipschitz condition, this paper concludes that the θ-Milstein method can capture the stability for ∈ 2 [1=2, 1]. Finally, an example is presented to illustrate the result.
