Analysis of stochastic time series in the presence of strong measurement noise

TL;DR

This paper introduces a novel method to analyze Langevin-type stochastic processes affected by strong Gaussian measurement noise, enabling extraction of noise parameters and approximations of drift and diffusion functions.

Contribution

It presents a new approach that allows for the characterization of measurement noise and the underlying stochastic dynamics despite strong noise interference.

Findings

Successfully extracts noise strength and correlation time.

Provides polynomial approximations of drift and diffusion functions.

Effective for Gaussian, exponentially correlated measurement noise.

Abstract

A new approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For the case of Gaussian distributed, exponentially correlated, measurement noise it is possible to extract the strength and the correlation time of the noise as well as polynomial approximations of the drift and diffusion functions from the underlying Langevin equation.