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.

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• Sparse inference and active learning of stochastic differential equations from data
• Theoretical results on the topological properties of the limited penetrable horizontal visibility graph family
• Arbitrary-order finite-time corrections for the Kramers-Moyal operator
• Magnetospheric Multiscale Observations of Markov Turbulence on Kinetic Scales
• Discontinuous Jump Behavior of the Energy Conversion in Wind Energy Systems
• Statistical analysis of stochastic magnetic fluctuations in space plasma based on the MMS mission
• Testing for Markovian character of transfer of fluctuations in solar wind turbulence on kinetic scales
• IntLevPy: A Python library to classify and model intermittent and Lévy processes
• Assessing Position-Dependent Diffusion from Biased Simulations and Markov State Model Analysis