一类带加性时空白噪声的随机双曲方程的唯一遍历性
偏微分方程分析
2021-09-08 v4 概率论
摘要
在本文中，我们考虑定义在维环面上的某类带阻尼和时空白噪声强迫的二阶非线性偏微分方程。该类方程包括时的波动方程和时的梁方程。我们证明无强迫无阻尼时方程的吉布斯测度是该系统流的唯一不变测度。由于该流不满足强Feller性质，我们引入了一种证明唯一遍历性的新技术。该方法在可能出现有限时间爆破的情形中也可能有用。
引用
@article{arxiv.1811.06294,
title = {Unique ergodicity for a class of stochastic hyperbolic equations with additive space-time white noise},
author = {Leonardo Tolomeo},
journal= {arXiv preprint arXiv:1811.06294},
year = {2021}
}
备注
The title has being changed from "Unique ergodicity for stochastic hyperbolic equations with additive space-time white noise" to "Unique ergodicity for a class of stochastic hyperbolic equations with additive space-time white noise", many typo corrections, some minor corrections in the proofs