Inhomogeneous functionals and approximations of invariant distributions of ergodic diffusions: Central limit theorem and moderate deviation asymptotics
Inhomogeneous functionals and approximations of invariant distributions of ergodic diffusions: Central limit theorem and moderate deviation asymptotics
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DOI：
10.1016/j.spa.2020.10.009
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发表时间：
2021-03-01
影响因子：
1.4
通讯作者：
Sundar, P.
中科院分区：
文献类型：
--
作者：
Ganguly, Arnab;Sundar, P.
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。通过选取适当的离散化步骤，证明了其收敛于不变分布的相应泛函，并利用中心极限定理和适度偏差原理分析了波动。这些结果对于理解基于欧拉离散的近似遍历扩散不变分布泛函的数值格式的准确性特别有用。这是一个无限时间视界问题，在这种情况下，数值格式的准确性比用于在有限时间间隔内产生近似扩散轨迹的格式研究得要少得多。这些结果的潜在应用也扩展到其他领域，包括数学物理，遍历扩散的参数推断和多尺度动力系统的平均分析。(C) 2020 Elsevier B.V.版权所有
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. (C) 2020 Elsevier B.V. All rights reserved.