随机动力系统的Wong-Zakai逼近

批准号:
11971186
项目类别:
面上项目
资助金额:
52.0 万元
负责人:
刘显明
依托单位:
学科分类:
动力系统与遍历论
结题年份:
2023
批准年份:
2019
项目状态:
已结题
项目参与者:
刘显明
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中文摘要
Wong-Zakai逼近通过对噪声磨光构造了逐轨道的确定系统,建立了确定方程和随机方程的解的逼近关系,在随机数值模拟、支撑定理、物理、滤波问题、工程问题等方面都有重要应用。前期研究中,我们首次将Wong-Zakai逼近的思想用于研究随机动力系统的不变集,在高斯噪声驱动随机偏微分方程的随机稳定流形、不变叶层和随机吸引子的上半连续性等方面取得了一系列成果,建立了确定动力系统和随机动力系统不变集的逼近关系。本项目拟在前期研究基础上,引入Skorokhod M-拓扑克服连续函数逼近右连左极函数的困难,利用Wong-Zakai逼近这一有力工具进一步研究非高斯列维噪声驱动的随机偏微分方程的不变集和不变测度。本项目的研究不仅能加深对非高斯随机动力系统的理解,而且将侧重于使用弱彩色噪声的多尺度物理模型积分O-U过程磨光列维过程,在理论和实际应用中都具有重要意义。
英文摘要
By smoothing the noise, Wong and Zakai constructed a sequence of sample-wise deterministic systems to approximate the original stochastic system and built a bridge between the sample-wise system and the original stochastic system. It has many important applications including stochastic numerical simulations, support theorems, filtering problems or to engineering and physical sciences etc. In the previous work, we have used the Wong-Zakai approximation to study the random invariant sets to systems driven by Wiener processes. We have established the Wong-Zakai approximation results to random stable manifolds and random invariant foliations of the stochastic partial differential equations driven by Gaussian noise, and have also studied the upper semi-continuity of the random pullback attractors. The approximation relationship between the deterministic dynamical systems and the random dynamical systems has been established. Based on the previous research, this project proposes to study the Wong-Zakai approximation of stochastic partial differential equations driven by Levy processes under the Skorokhod M-topology. With the powerful Wong-Zakai approach, we will then study the random invariant manifolds, random attractors and other random invariant sets and invariant measures of stochastic partial differential equations driven by Levy processes. We will focus on the integrated Ornstein-Uhlenbeck processes approximation, which is the multi-time-scale physical model of weakly colored noises and is also an important Wong-Zakai type approximation. Therefore, it will be helpful for us to understand the relationship between stochastic dynamical systems and deterministic dynamical systems more deeply in the proposed project, which has great significance in both theoretical and practical applications.
期刊论文列表
专著列表
科研奖励列表
会议论文列表
专利列表
DOI:10.1016/j.jde.2022.01.024
发表时间:2022-03
期刊:Journal of Differential Equations
影响因子:2.4
作者:Xianming Liu
通讯作者:Xianming Liu
DOI:10.3934/dcdsb.2020192
发表时间:2021
期刊:Discrete and Continuous Dynamical Systems-Series B
影响因子:--
作者:Liu Xianming;Han Guangyue
通讯作者:Han Guangyue
DOI:10.1016/j.spa.2021.12.016
发表时间:2022-01
期刊:Stochastic Processes and their Applications
影响因子:1.4
作者:Xianming Liu
通讯作者:Xianming Liu
DOI:https://doi.org/10.1016/j.jmaa.2021.125642
发表时间:2022
期刊:J. Math. Anal. Appl.
影响因子:--
作者:Liu Xianming
通讯作者:Liu Xianming
DOI:DOI: 10.1142/S0219493723400051
发表时间:2023
期刊:Stochastics and Dynamics
影响因子:1.1
作者:Feng Lingyu;Gao Ting;Li Ting;Lin Zhongjie;Liu Xianming
通讯作者:Liu Xianming
非高斯过程驱动系统的随机不变流形
- 批准号:11301197
- 项目类别:青年科学基金项目
- 资助金额:22.0万元
- 批准年份:2013
- 负责人:刘显明
- 依托单位:
国内基金
海外基金
