带Poisson跳和Markovian转换的随机时滞泛函微分方程数值解的收敛性

为了近一步研究带Poisson跳和Markovian转换的随机时滞泛函微分方程数值解的收敛性问题，文中给出带Poisson跳和 Markovian 转换的随机时滞泛函微分方程 Euler 数值解迭代格式。在弱条件下，利用Laypunov泛函方法和随机分析理论证明了数值解依概率收敛于方程的解。所得结果覆盖了许多非线性时滞微分方程已经存在的某些理论，而且实验说明此结论比以往的结论更容易验证。

Convergence of numerical solution to stochastic delay functional differential equations with Poisson j ump and Markovian switching

In order to further study the convergence of numerical solution to stochastic delay functional differential equations with Poisson j ump and Markovian switching,a numerical ap-proximation scheme is proposed to approximates the solution of stochastic delay functional dif-ferential equations with Poisson j ump and Markovian switching.It is proved that the Euler ap-proximation solution converges to the analytic solution in probability under weaker conditions, mainly by using the Lyapunov function method and the stochastic analysis theory.The results not only cover many highly non-linear stochastic differential equcetions,but it can also be veri-fied easily than the known results.