Numerical stationary distribution and its convergence for nonlinear stochastic differential equations
Numerical stationary distribution and its convergence for nonlinear stochastic differential equations
复制标题
DOI：
10.1016/j.cam.2014.08.019
复制
发表时间：
2015-03
期刊：
影响因子：
--
通讯作者：
W. Liu;X. Mao
中科院分区：
文献类型：
--
作者：
W. Liu;X. Mao
为了避免通过求解非平凡Kolmogorov-Fokker-Planck方程来求随机微分方程的平稳分布，采用数值平稳分布作为近似。本文用后向欧拉-丸山方法逼近方程的平稳分布。目前已有的结果（Mao et al.，2005; Yuan等人，2005; Yuan等人，2004）的范围进行了扩展，以涵盖更大的范围内的非线性方程组时，漂移系数的线性增长条件被违反。
To avoid finding the stationary distributions of stochastic differential equations by solving the nontrivial Kolmogorov–Fokker–Planck equations, the numerical stationary distributions are used as the approximations instead. This paper is devoted to approximate the stationary distribution of the underlying equation by the Backward Euler–Maruyama method. Currently existing results (Mao et al., 2005; Yuan et al., 2005; Yuan et al., 2004) are extended in this paper to cover larger range of nonlinear SDEs when the linear growth condition on the drift coefficient is violated.