Large deviations for interacting multiscale particle systems
Large deviations for interacting multiscale particle systems
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DOI：
10.1016/j.spa.2022.09.010
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发表时间：
2020-11
影响因子：
1.4
通讯作者：
Zachary Bezemek;K. Spiliopoulos
中科院分区：
文献类型：
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作者：
Zachary Bezemek;K. Spiliopoulos
本文考虑一组在双尺度局部周期环境中运动的弱相互作用扩散过程。研究了当粒子数趋于无穷大，时标分离参数趋于零时，粒子位置在组合极限下的经验分布的大偏差原理.我们利用弱收敛方法提供了一个方便的表示大偏差率函数，这使我们能够有效地控制平均场动力学的特点。此外，我们严格地获得等价的非变分表示的大偏差率函数介绍的道森-Gärtner。
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles’ positions in the combined limit as the number of particles grow to infinity and the time-scale separation parameter goes to zero. We make use of weak convergence methods providing a convenient representation for the large deviations rate function, which allow us to characterize the effective controlled mean field dynamics. In addition, we rigorously obtain equivalent non-variational representations for the large deviations rate function as introduced by Dawson–Gärtner.