Unbiased estimate of forces from measured correlation functions, including the case of strong multiplicative noise

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Abstract

Starting from appropriate short-time correlation function measurements, we propose a dynamical “learning” method to derive the deterministic and stochastic forces underlying an observed process, even if this process contains strong multiplicative noise. To do this we extend the ideas of our previous paper [1] to establish mathematical relationships in this more general case between the joint distribution function of the process and its corresponding Ito-Langevin equation. A numerical example for a simulated process containing strong multiplicative noise shows good agreement with the theory.

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