非线性混杂随机泛函微分方程解的收敛性分析

Convergence Analysis of Solutions of Nonlinear Hybrid Stochastic Functional Differential Equations

现有的非线性混杂随机泛函微分方程解的收敛性分析方法存在均方稳定性较低的缺点,为解决该问题,提出新的非线性混杂随机泛函微分方程解收敛性分析方法。构建非线性混杂随机泛函微分方程,采用截断E-M算法计算方程解,分析方程的p阶有界性,证明方程解的唯一性,引入四个定理证明方程解的收敛性,实现了非线性混杂随机泛函微分方程解的收敛性分析。测试结果表明,研究方法极大地提升了均方稳定性,具备更好的方程解收敛性分析性能。

The existing convergence analysis methods for nonlinear hybrid stochastic functional differential equations have low mean square stability,in order to solve this problem,a new method of convergence analysis of nonlinear hybrid stochastic functional differential equation is proposed.The nonlinear hybrid random functional differential equation is constructed,the solution of the equation is calculated by truncating E-M algorithm,the p-th order boundedness of the equation is analyzed,the uniqueness of the solution of the equation is proved,and the convergence of the solution of the nonlinear hybrid random functional differential equation is analyzed by introducing four theorems to prove the convergence of the solution of the equation.The test results show that the method greatly improves the mean square stability and has better performance in the convergence analysis of the equation solutions.