论文标题
非线性随机延迟微分方程的明确近似值的强收敛和稳定性
The Strong Convergence and Stability of Explicit Approximations for Nonlinear Stochastic Delay Differential Equations
论文作者
论文摘要
本文着重于非线性随机延迟微分方程（SDDE）的明确近似值。在弱的本地Lipschitz和一些合适的条件下，提出了SDDES的通用截短的Euler-Maruyama（TEM）方案，该方案将数值溶液界定并收敛到QTH时刻的精确溶液中，qTh时刻> 0。此外，产生1/2阶收敛速率。在Khasminskii-type条件下，给出了更精确的TEM方案，该方案在均方和P-1中的数值溶液在指数方面稳定。最后，进行了几项数值实验，以说明我们的结果。
This paper focuses on explicit approximations for nonlinear stochastic delay differential equations (SDDEs). Under the weakly local Lipschitz and some suitable conditions, a generic truncated Euler-Maruyama (TEM) scheme for SDDEs is proposed, which numerical solutions are bounded and converge to the exact solutions in qth moment for q>0. Furthermore, the 1/2 order convergent rate is yielded. Under the Khasminskii-type condition, a more precise TEM scheme is given, which numerical solutions are exponential stable in mean square and P-1. Finally, several numerical experiments are carried out to illustrate our results.
