The Langevin Approach: An R Package for Modeling Markov 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.

Keywords

• R
• stochastic processes
• Markov processes
• data analysis
• time series