Analysis of data sets of stochastic systems

TL;DR

This paper presents a method to extract drift and diffusion terms from noisy data of stochastic systems described by Langevin equations, enabling identification of underlying deterministic and stochastic forces.

Contribution

It introduces a novel technique for analyzing noisy data to determine the dynamics of stochastic systems modeled by Langevin equations.

Findings

Successfully applied to simulated data sets

Accurately extracts drift and diffusion terms

Validates method for one- and two-dimensional systems

Abstract

This paper deals with the analysis of stochastic systems which can be described by a Langevin equation. By the method presented in this paper drift and diffusion terms of the corresponding Fokker-Planck equation can be extracted from the noisy data sets, and deterministic laws and fluctuating forces of the dynamics can be identified. The method is validated by the application to simulated one- and two-dimensional noisy data sets.