On the identifiability of interaction functions in systems of interacting particles
On the identifiability of interaction functions in systems of interacting particles
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DOI：
10.1016/j.spa.2020.10.005
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发表时间：
2019-12
影响因子：
1.4
通讯作者：
Zhongyan Li;F. Lu;M. Maggioni;Sui Tang;C. Zhang
中科院分区：
文献类型：
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作者：
Zhongyan Li;F. Lu;M. Maggioni;Sui Tang;C. Zhang
我们解决一个基本问题，在相互作用粒子系统的非参数推断：相互作用函数的可识别性。我们证明了一类一阶随机系统的相互作用函数是可识别的，包括具有一般初始律的线性系统和具有平稳分布的非线性系统。我们证明了一个可识别性条件是足够的，并成为必要的粒子数接近无穷大时。该性质等价于相关积分算子的严格正性，并利用Müntz型定理证明了其积分核是严格正定的.
We address a fundamental issue in the nonparametric inference for systems of interacting particles: the identifiability of the interaction functions. We prove that the interaction functions are identifiable for a class of first-order stochastic systems, including linear systems with general initial laws and nonlinear systems with stationary distributions. We show that a coercivity condition is sufficient for identifiability and becomes necessary when the number of particles approaches infinity. The coercivity is equivalent to the strict positivity of related integral operators, which we prove by showing that their integral kernels are strictly positive definite by using Müntz type theorems.