论文标题
使用自适应EM方法在有限和无限视野中的SDDE的显式数值近似值：强烈的收敛性和几乎确定的指数稳定性
Explicit Numerical Approximations for SDDEs in Finite and Infinite Horizons using the Adaptive EM Method: Strong Convergence and Almost Sure Exponential Stability
论文作者
论文摘要
在本文中，我们通过使用自适应的Euler-Maruyama（EM）方法研究了在局部Lipschitz条件下随机微分延迟方程（SDDE）的显式数值近似值。在有限和无限的视野中，我们通过显示自适应EM溶液的PTH矩的界限来实现强大的收敛结果。我们还获得了无限范围收敛的顺序。此外，我们显示了SDE和SDDE的自适应近似解决方案的几乎确定的指数稳定性。
In this paper we investigate explicit numerical approximations for stochastic differential delay equations (SDDEs) under a local Lipschitz condition by employing the adaptive Euler-Maruyama (EM) method. Working in both finite and infinite horizons, we achieve strong convergence results by showing the boundedness of the pth moments of the adaptive EM solution. We also obtain the order of convergence infinite horizon. In addition, we show almost sure exponential stability of the adaptive approximate solution for both SDEs and SDDEs.
