论文标题
超线性随机功能微分方程的显式近似
An explicit approximation for super-linear stochastic functional differential equations
论文作者
论文摘要
由于很难在无限维空间上实施隐式方案，因此我们旨在开发近似超线性随机功能差分方程（SFDES）的显式数值方法。确切地说，借用截断的想法和线性插值，我们提出了一个明确的截短的Euler-Maruyama方案，用于超级线性SFDES，并在l^p中获得界限和收敛性。我们还以1/2顺序产生收敛速率。与以前的一些作品不同，我们释放了全局Lipschitz对扩散系数的限制。此外，我们揭示了数值解决方案可以保留基本的指数稳定性。此外，我们举了几个示例来支持我们的理论。
Since it is difficult to implement implicit schemes on the infinite-dimensional space, we aim to develop the explicit numerical method for approximating super-linear stochastic functional differential equations (SFDEs). Precisely, borrowing the truncation idea and linear interpolation we propose an explicit truncated Euler-Maruyama scheme for super-linear SFDEs, and obtain the boundedness and convergence in L^p. We also yield the convergence rate with 1/2 order. Different from some previous works, we release the global Lipschitz restriction on the diffusion coefficient. Furthermore, we reveal that numerical solutions preserve the underlying exponential stability. Moreover, we give several examples to support our theory.
