The Langevin Approach: An R Package for Modeling Markov Processes

TL;DR

This paper introduces an R package that models Markov processes from data by extracting underlying stochastic differential equations, applicable to one- or two-dimensional datasets, with validation procedures and extensions for non-ideal conditions.

Contribution

The paper presents a new R package for deriving stochastic differential equations from data, including validation steps and methods for non-Markovian or non-Gaussian cases.

Findings

Successfully extracts stochastic equations from data sets

Provides validation procedures for model assumptions

Discusses extensions for complex stochastic processes

Abstract

We describe an R package developed by the research group Turbulence, Wind energy and Stochastics (TWiSt) at the Carl von Ossietzky University of Oldenburg, which extracts the (stochastic) evolution equation underlying a set of data or measurements. The method can be directly applied to data sets with one or two stochastic variables. Examples for the one-dimensional and two-dimensional cases are provided. This framework is valid under a small set of conditions which are explicitly presented and which imply simple preliminary test procedures to the data. For Markovian processes involving Gaussian white noise, a stochastic differential equation is derived straightforwardly from the time series and captures the full dynamical properties of the underlying process. Still, even in the case such conditions are not fulfilled, there are alternative versions of this method which we discuss briefly and provide the user with the necessary bibliography.