Kramers---Moyal =============== .. toctree:: :maxdepth: 2 :code:`kramersmoyal` is a python package designed to obtain the Kramers---Moyal coefficients, or conditional moments, from stochastic data of any dimension. It employs kernel density estimations, instead of a histogram approach, to ensure better results for low number of points as well as allowing better fitting of the results. .. include:: installation.rst .. include:: 1dprocess.rst .. include:: 2dprocess.rst Table of Content ================ .. toctree:: :maxdepth: 3 installation 1dprocess 2dprocess functions/index license Literature ========== :sup:`1` Friedrich, R., Peinke, J., Sahimi, M., Tabar, M. R. R. *Approaching complexity by stochastic methods: From biological systems to turbulence,* [Phys. Rep. 506, 87–162 (2011)](https://doi.org/10.1016/j.physrep.2011.05.003). The study of stochastic processes from a data-driven approach is grounded in extensive mathematical work. From the applied perspective there are several references to understand stochastic processes, the Fokker---Planck equations, and the Kramers---Moyal expansion | Tabar, M. R. R. (2019). *Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems.* Springer, International Publishing | Risken, H. (1989). *The Fokker–Planck equation.* Springer, Berlin, Heidelberg. | Gardiner, C.W. (1985). *Handbook of Stochastic Methods.* Springer, Berlin. An extensive review on the subject can be found `here `_. Funding ======= Helmholtz Association Initiative *Energy System 2050 - A Contribution of the Research Field Energy* and the grant No. VH-NG-1025 and *STORM - Stochastics for Time-Space Risk Models* project of the Research Council of Norway (RCN) No. 274410.