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

TL;DR

This paper extends a method for analyzing multi-dimensional stochastic processes affected by strong, correlated measurement noise, enabling extraction of noise characteristics and approximations of the underlying process's drift and diffusion functions.

Contribution

It generalizes a recent approach to handle N-dimensional processes with strong, correlated Gaussian noise, providing a way to estimate noise parameters and process functions.

Findings

Successfully extracts noise strength and correlation functions.

Provides polynomial approximations of drift and diffusion functions.

Applicable to high-dimensional stochastic data with strong noise.

Abstract

An extension and generalization of a recently presented approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For a stochastic process in N dimensions which is superimposed with strong, exponentially correlated, Gaussian distributed, measurement noise it is possible to extract the strength and the correlation functions of the noise as well as polynomial approximations of the drift and diffusion functions of the underlying process.