熵多种群动力系统的平均场极限。

IF 1.2 3区数学 Q1 MATHEMATICS

Milan Journal of Mathematics Pub Date : 2023-01-01 DOI:10.1007/s00032-022-00375-w

Stefano Almi, Claudio D'Eramo, Marco Morandotti, Francesco Solombrino

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引用次数: 1

摘要

在一般假设条件下，证明了具有熵正则化的多种群动力系统的适定性及其收敛于合适的平均场近似。在进一步假设标签演化的前提下，考虑了智能体位置和标签动态之间存在不同时间尺度的情况。该极限系统耦合了位置空间中的平均场型演化和标签空间中收益泛函的瞬时优化。

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Mean-Field Limits for Entropic Multi-Population Dynamical Systems.

The well-posedness of a multi-population dynamical system with an entropy regularization and its convergence to a suitable mean-field approximation are proved, under a general set of assumptions. Under further assumptions on the evolution of the labels, the case of different time scales between the agents' locations and labels dynamics is considered. The limit system couples a mean-field-type evolution in the space of positions and an instantaneous optimization of the payoff functional in the space of labels.

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来源期刊

Milan Journal of Mathematics 数学-数学

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Milan Journal of Mathematics (MJM) publishes high quality articles from all areas of Mathematics and the Mathematical Sciences. The authors are invited to submit "articles with background", presenting a problem of current research with its history and its developments, the current state and possible future directions. The presentation should render the article of interest to a wider audience than just specialists. Many of the articles will be "invited contributions" from speakers in the "Seminario Matematico e Fisico di Milano". However, also other authors are welcome to submit articles which are in line with the "Aims and Scope" of the journal.