Empirical approximation to invariant measures for McKean–Vlasov processes: Mean-field interaction vs self-interaction

IF 1.5 2区 数学 Q2 STATISTICS & PROBABILITY
Bernoulli Pub Date : 2021-12-28 DOI:10.3150/22-bej1550
Kai Du, Yifan Jiang, Jinfeng Li
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引用次数: 4

Abstract

This paper proves that, under a monotonicity condition, the invariant probability measure of a McKean--Vlasov process can be approximated by weighted empirical measures of some processes including itself. These processes are described by distribution dependent or empirical measure dependent stochastic differential equations constructed from the equation for the McKean--Vlasov process. Convergence of empirical measures is characterized by upper bound estimates for their Wasserstein distance to the invariant measure. The theoretical results are demonstrated via a mean-field Ornstein--Uhlenbeck process.
McKean–Vlasov过程不变测度的经验近似:平均场相互作用与自相互作用
本文证明了在单调性条件下,McKean—Vlasov过程的不变概率测度可以用包括其自身在内的一些过程的加权经验测度来近似。这些过程由分布相关或经验测度相关的随机微分方程描述,该方程由McKean-Vlasov过程的方程构造。经验测度的收敛性以其到不变测度的Wasserstein距离的上界估计为特征。理论结果通过平均场Ornstein-Uhlenbeck过程得到了证明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Bernoulli
Bernoulli 数学-统计学与概率论
CiteScore
3.40
自引率
0.00%
发文量
116
审稿时长
6-12 weeks
期刊介绍: BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. BERNOULLI will publish: Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed. Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research: Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historical significant aspect of statistics and probability.
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