扰动线性随机泛函微分方程均方渐近稳定性的刻画
概率论
2023-06-19 v3 动力系统
摘要
本文研究了一类扰动标量线性随机泛函微分方程的均方渐近稳定性。具体而言,我们给出了强迫项满足均方收敛、均方指数收敛以及解均方可积性的充要条件。这些结论成立的前提是底层未扰动的 SFDE 是均方渐近稳定的。
引用
@article{arxiv.2304.08161,
title = {Mean square asymptotic stability characterisation of perturbed linear stochastic functional differential equations},
author = {John Appleby and Emmet Lawless},
journal= {arXiv preprint arXiv:2304.08161},
year = {2023}
}
备注
36 pages, to appear in Applied Numerical Mathematics as part of the conference proceedings for FAATNA (Functional Analysis, Approximation Theory and Numerical Analysis), Matera Italy, July 2022