关键词: 随机变延迟微分方程, 指数Euler方法, Lipschitz条件, It公式, 强收敛性

Abstract:

The authors used the exponential Euler method to make the numerical solution convergence for semi\|linear stochastic variable delay differential
equation under the global Lipschitz condition and the linear growth condition, and the numerical solutions converge to the exact solution. The convergence order is 1/2min{1,γ}, γ∈(0,1］.

Key words: stochastic variable delay differential equation, exponential Euler method, Lipschitz condition, It formula, strong convergence