Overview

Understanding complex processes in nature often necessitates describing them as stochastic processes that split the dynamics into a deterministic and a fluctuating part.

The coefficients that quantify these stochastic processes can be obtained from time series via the Kramers-Moyal expansion.
Deriving these Kramal-Moyal Coefficients makes valuable insights into the underlying dynamics accessible.

The Python package kramersmoyal offers a comprehensive way to derive these coefficients for multi-dimensional time series.
It was developed at the Institute of Energy and Climate Research at the Forschungszentrum Jülich GmbH and is available at github.com/LRydin/KramersMoyal.
It can be installed via pip from PyPI (pypi.org/project/kramersmoyal/).

Some basic examples of how to use kramersmoyal can be found in the Github repository and documentation is available at kramersmoyal.readthedocs.io. Specifically, an example of a one-dimensional and a two-dimensional stochastic process is provided both in the documentation and as a jupyter notebook kmc.ipynb.

A more detailed description of the package and the underlying theory is published in the peer-reviewed article in the The Journal of Open Source Software (DOI: 10.21105/joss.01693).

Citation

If you use kramersmoyal in your research, please cite it as:

Rydin Gorjão, L., and Meirinhos, F. (2019). kramersmoyal: Kramers--Moyal coefficients for stochastic processes. Journal of Open Source Software, 4(44), 1693. DOI: 10.21105/joss.01693

Acknowlegments

The authors acknowledge the funding by the Helmholtz Association vias the Initiative Energy System 2050 - A Contribution of the Research Field Energy, grant No. VH-NG-1025, and STORM - Stochastics for Time-Space Risk Models project of the Research Council of Norway (RCN) No. 274410.