Nonparametric inference for diffusion processes in systems with smooth evolution

Abstract

Dynamics of complex systems can often be successfully modeled as a stochastic diffusion process, even if the real dynamics are not strictly diffusive. We show that for such systems current methods for nonparametric estimation of the drift and diffusion terms may lead to results that are inconsistent with the probability distribution of the system. We present a novel estimation technique that for the two systems studied, turbulent flow and molecular motion in gas, produces drift and diffusion consistent with the observed probability density functions. The presented method is applicable to systems with smooth real dynamics.