刘瑶, 谢颖超, 张梦鸽. 一类平均场随机微分方程的遍历性[J]. 应用概率统计, 2023, 39(6): 897-906. DOI: 10.3969/j.issn.1001-4268.2023.06.008
引用本文: 刘瑶, 谢颖超, 张梦鸽. 一类平均场随机微分方程的遍历性[J]. 应用概率统计, 2023, 39(6): 897-906. DOI: 10.3969/j.issn.1001-4268.2023.06.008
LIU Yao, XIE Yingchao, ZHANG Mengge. Ergodicity of a Class of Mean Filed SDEs[J]. Chinese Journal of Applied Probability and Statistics, 2023, 39(6): 897-906. DOI: 10.3969/j.issn.1001-4268.2023.06.008
Citation: LIU Yao, XIE Yingchao, ZHANG Mengge. Ergodicity of a Class of Mean Filed SDEs[J]. Chinese Journal of Applied Probability and Statistics, 2023, 39(6): 897-906. DOI: 10.3969/j.issn.1001-4268.2023.06.008

一类平均场随机微分方程的遍历性

Ergodicity of a Class of Mean Filed SDEs

  • 摘要: 本文研究了一类一维带平均场的非时齐随机微分方程.在一定条件下, 我们证明了方程唯一解的遍历性. 进一步地,当平均场强度趋于~0~时, 我们还证明了方程的解和平稳分布分别几乎一致、依~Wasserstein~距离收敛于相应无平均场方程的解和平稳分布.

     

    Abstract: In this paper, we study a class of one-dimensional time-inhomogeneous stochastic differential equations with mean field. We show that the unique solution is ergodic under certain conditions. We further show that, as the strength of the mean field tends to 0, the solution and stationary distribution of such equation respectively converge a.e. \!\!uniformly and in Wasserstein distance to those of corresponding equation without mean field.

     

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