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
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
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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