Journal
STOCHASTICS AND DYNAMICS
Volume -, Issue -, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219493723400038
Keywords
Identifiability; positive definite kernels; interacting particle systems; ergodicity
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This study proves the coercivity condition for stochastic systems with an arbitrary number of particles and a class of kernels, where the system of relative positions is ergodic. In the stationary case, the coercivity condition is proven by showing the positive definiteness of an integral kernel. For the non-stationary case, it is shown that the coercivity condition holds when the time is large based on a perturbation argument.
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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