Parameter-free resolution of the superposition of stochastic signals

TL;DR

This paper introduces a parameter-free method to separate and identify the deterministic and stochastic components of combined stochastic signals, including Ornstein-Uhlenbeck and non-linear Langevin processes, directly from empirical data.

Contribution

It extends a recent Langevin analysis approach to handle superimposed stochastic signals without requiring prior parameter knowledge.

Findings

Method accurately separates stochastic components in synthetic data

Successfully retrieves stochastic evolution equations from empirical data

Handles complex superpositions of stochastic processes

Abstract

This paper presents a direct method to obtain the deterministic and stochastic contribution of the sum of two independent sets of stochastic processes, one of which is composed by Ornstein-Uhlenbeck processes and the other being a general (non-linear) Langevin process. The method is able to distinguish between all stochastic process, retrieving their corresponding stochastic evolution equations. This framework is based on a recent approach for the analysis of multidimensional Langevin-type stochastic processes in the presence of strong measurement (or observational) noise, which is here extended to impose neither constraints nor parameters and extract all coefficients directly from the empirical data sets. Using synthetic data, it is shown that the method yields satisfactory results.