相互作用粒子系统学习中的矫顽力条件

IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
Zhongyang Li, Fei Lu
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引用次数: 4

摘要

在粒子或智能体相互作用系统的推理中,矫顽力条件保证了相互作用核的可辨识性,为学习提供了基础。我们证明了具有任意数目粒子和一类核的随机系统的矫顽力条件,使得相对位置系统是遍历的。当相对位置系统是平稳时,我们通过证明学习中出现的积分核的严格正定性来证明矫顽性条件。对于非平稳情况,我们基于摄动论证证明了当时间较大时,矫顽力条件成立。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the coercivity condition in the learning of interacting particle systems
In the inference for systems of interacting particles or agents, a coercivity condition ensures the identifiability of the interaction kernels, providing the foundation of learning. We prove the coercivity condition for stochastic systems with an arbitrary number of particles and a class of kernels such that the system of relative positions is ergodic. When the system of relative positions is stationary, we prove the coercivity condition by showing the strictly positive definiteness of an integral kernel arising in the learning. For the non-stationary case, we show that the coercivity condition holds when the time is large based on a perturbation argument.
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来源期刊
Stochastics and Dynamics
Stochastics and Dynamics 数学-统计学与概率论
CiteScore
1.70
自引率
0.00%
发文量
49
审稿时长
>12 weeks
期刊介绍: This interdisciplinary journal is devoted to publishing high quality papers in modeling, analyzing, quantifying and predicting stochastic phenomena in science and engineering from a dynamical system''s point of view. Papers can be about theory, experiments, algorithms, numerical simulation and applications. Papers studying the dynamics of stochastic phenomena by means of random or stochastic ordinary, partial or functional differential equations or random mappings are particularly welcome, and so are studies of stochasticity in deterministic systems.
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