# The Langevin Approach: An R Package for Modeling Markov Processes

@article{Rinn2016TheLA, title={The Langevin Approach: An R Package for Modeling Markov Processes}, author={Philip Rinn and Pedro G. Lind and Matthias Wachter and Joachim Peinke}, journal={Journal of open research software}, year={2016}, volume={4} }

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…

## 25 Citations

### PyDaddy: A Python package for discovering stochastic dynamical equations from timeseries data

- Computer ScienceArXiv
- 2022

This work presents PyDaddy, a toolbox to construct and analyze interpretable SDE models based on time-series data, and combines traditional approaches for data-driven SDE reconstruction with an equation learning approach, to derive symbolic equations governing the stochastic dynamics.

### Arbitrary-Order Finite-Time Corrections for the Kramers–Moyal Operator

- MathematicsEntropy
- 2021

With the aim of improving the reconstruction of stochastic evolution equations from empirical time-series data, a full representation of the generator of the Kramers–Moyal operator is derived via a power-series expansion of the exponential operator, allowing for separate finite-time corrections of the power- series expansion of arbitrary order.

### Numerical Solution of Stochastic Differential Equations: Diffusion and Jump-Diffusion Processes

- MathematicsUnderstanding Complex Systems
- 2019

Stochastic differential equations (SDE) play an important role in a range of application areas, including biology, physics, chemistry, epidemiology, mechanics, microelectronics, economics, and…

### Fractional Brownian motion inference of multivariate stochastic differential equations

- Mathematics
- 2020

Recently, the financial mathematics has been emerged to interpret and predict the underlying mechanism that generates an incident of concern. A system of differential equations can reveal a dynamical…

### Modellierung von Windgeschwindigkeiten mit Hilfe der Langevin Gleichung Bachelorarbeit

- Mathematics
- 2018

Wind data is a stochastic process that cannot be modelled by a deterministic function alone. However, due to ever more demanding need for renewable and clean energy, wind power needs to be…

### Bayesian inference of fractional brownian motion of multivariate stochastic differential equations

- Mathematics
- 2021

There have been much interest in analysis of stochastic differential equation with long memory, represented by fractional diffusion process, this property have been proved itself in financial…

### Stochastic modelling of non-stationary financial assets.

- MathematicsChaos
- 2017

The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of values.

### Disentangling stochastic signals superposed on short localized oscillations

- Computer Science
- 2020

### Reconstruction of Stochastic Dynamical Equations: Exemplary Diffusion, Jump-Diffusion Processes and Lévy Noise-Driven Langevin Dynamics

- MathematicsUnderstanding Complex Systems
- 2019

In this chapter we reconstruct stochastic dynamical equations with known drift and diffusion coefficients, as well as known properties of jumps, jump amplitude and jump rate from synthetic time…

### Data-Driven Model of the Power-Grid Frequency Dynamics

- EngineeringIEEE Access
- 2020

An easy-to-use, data-driven, stochastic model for the power-grid frequency is introduced and it is demonstrated how it reproduces key characteristics of the observed statistics of the Continental European and British power grids.

## References

SHOWING 1-10 OF 36 REFERENCES

### Experimental indications for Markov properties of small scale turbulence

- Physics
- 2001

There is evidence that the statistics of the longitudinal velocity increment v(r) can be described as a Markov process, and knowledge of the Fokker{Planck equation allows the joint probability density of N increments on N dierent scales p(v1;r1;:::;vN;rN) to be determined.

### Towards a stochastic multi-point description of turbulence

- Physics
- 2010

In previous work it was found that the multi-scale statistics of homogeneous isotropic turbulence can be described by a stochastic "cascade" process of the velocity increment from scale to scale,…

### Estimation of drift and diffusion functions from time series data: a maximum likelihood framework.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

This paper develops a framework for the estimation of the functions and their respective (Bayesian posterior) confidence regions based on likelihood estimators and solves important problems concerning the applicability and the accuracy of estimated parameters.

### Markov properties in presence of measurement noise.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

It is demonstrated that the presence of measurement noise, likewise, spoils Markov properties of an underlying Markov process, which is promising for the further development of techniques for the reconstruction of stochastic processes from measured data.

### The Fokker-Planck Equation

- Physics
- 2010

In 1984, H. Risken authored a book (H. Risken, The Fokker-Planck Equation: Methods of Solution, Applications, Springer-Verlag, Berlin, New York) discussing the Fokker-Planck equation for one…

### Description of a Turbulent Cascade by a Fokker-Planck Equation

- Physics
- 1997

Fully developed turbulence is still regarded to be one of the main unsolved problems of classical physics. Great efforts have been made towards an understanding of small scale turbulent velocity…

### Stochastic analysis of ocean wave states with and without rogue waves

- Mathematics, Physics
- 2014

This work presents an analysis of ocean wave data including rogue waves. A stochastic approach based on the theory of Markov processes is applied. With this analysis we achieve a characterization of…

### Stochastic method for in-situ damage analysis

- Physics
- 2012

Based on the physics of stochastic processes we present a new approach for structural health monitoring. We show that the new method allows for an in-situ analysis of the elastic features of a…

### Estimation of Kramers-Moyal coefficients at low sampling rates.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

An optimization procedure for the estimation of Kramers-Moyal coefficients from stationary, one-dimensional, Markovian time series data is presented. The method takes advantage of a recently reported…