Abstract The paper studies asymptotics of inhomogeneous integral functionals of an ergodic diffusion process under the effect of discretization. Convergence to the corresponding functionals of the invariant distribution is shown for suitably chosen discretization steps, and the fluctuations are analyzed through central limit theorem and moderate deviation principle. The results will be particularly useful for understanding accuracy of an Euler discretization based numerical scheme for approximating functionals of invariant distribution of an ergodic diffusion. This is an infinite-time horizon problem, and the accuracy of numerical schemes in this context are comparatively much less studied than the ones used for generating approximate trajectories of diffusions over finite time intervals. The potential applications of these results also extend to other areas including mathematical physics, parameter inference of ergodic diffusions and analysis of multiscale dynamical systems with averaging.

中文翻译：

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遍历扩散不变分布的非齐次泛函和近似：中心极限定理和中度偏差渐近

摘要 本文研究了离散化作用下遍历扩散过程的非齐次积分泛函的渐近性。Convergence to the corresponding functionals of the invariant distribution is shown for suitably chosen discretization steps, and the fluctuations are analyzed through central limit theorem and moderate deviation principle. 结果对于理解基于欧拉离散化的数值方案的准确性特别有用，该方案用于逼近遍历扩散不变分布的函数。这是一个无限时间范围问题，与用于在有限时间间隔内生成近似扩散轨迹的数值方案相比，在这种情况下数值方案的准确性研究相对较少。