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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关于相互作用粒子系统学习中的矫顽力条件

在对相互作用的粒子或主体的系统进行推理时，矫顽力条件确保了相互作用核的可识别性，提供了学习的基础。我们证明了具有任意数量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。当相对位置系统静止时，我们通过证明学习中产生的积分核的严格正定性来证明矫顽力条件。对于非平稳情况，我们根据扰动论证证明，当时间较长时，矫顽力条件成立。