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On the identifiability of interaction functions in systems of interacting particles

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  • Li, Zhongyang
  • Lu, Fei
  • Maggioni, Mauro
  • Tang, Sui
  • Zhang, Cheng

Abstract

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.

Suggested Citation

  • Li, Zhongyang & Lu, Fei & Maggioni, Mauro & Tang, Sui & Zhang, Cheng, 2021. "On the identifiability of interaction functions in systems of interacting particles," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 135-163.
    • Handle: RePEc:eee:spapps:v:132:y:2021:i:c:p:135-163
    DOI: 10.1016/j.spa.2020.10.005
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    References listed on IDEAS

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    1. Jose Casadiego & Mor Nitzan & Sarah Hallerberg & Marc Timme, 2017. "Model-free inference of direct network interactions from nonlinear collective dynamics," Nature Communications, Nature, vol. 8(1), pages 1-10, December.
    2. Anatoli V. Skorokhod, 1996. "On the regularity of many-particle dynamical systems perturbed by white noise," International Journal of Stochastic Analysis, Hindawi, vol. 9, pages 1-11, January.
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    Cited by:

    1. Della Maestra, Laetitia & Hoffmann, Marc, 2023. "The LAN property for McKean–Vlasov models in a mean-field regime," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 109-146.

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