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    带跳的非线性随机延迟微分方程的Split-step算法

    Split-Step Method for Nonlinear Stochastic Delay Differential Equation with Jumps

    • 摘要: 研究了It意义下一类具有特殊情形的、带跳的非线性随机延迟微分方程的Split step算法,证明了该算法在均值意义下以1.5阶矩一致收敛,在均方意义下以1阶矩一致收敛;得到了Split step法均方稳定的条件,最后通过一些数值实例验证了算法的有效性。

       

      Abstract: This paper discusses split step algorithm for solving nonlinear stochastic delay differential equation with jumps in It sense. It is proved that the split step method is uniformly convergent with order of 1.5 in the mean sense and order of 1 in the mean square sense. The mean square stable of the split step method under some conditions is also obtained. Some numerical experiments are reported to testify the performance and effectiveness of this method in this paper.

       

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