kramersmoyal: Kramers--Moyal coefficients for stochastic processes
Leonardo Gorjão, Francisco Meirinhos · The Journal of Open Source Software · 2019
A general problem for evaluating Markovian stochastic processes is the retrieval of the moments or the Kramers-Moyal coefficients M from data or time-series.The Kramers-Moyal coefficients are derived from an Taylor expansion of the master equation that describes the probability evolution of a Markovian stochastic process.Given a set of stochastic data, ergodic or quasi-stationary, the extensive literature of stochastic processes awards a set of measures, such as the Kramers-Moyal coefficients or its moments, which link stochastic processes to a probabilistic description of the process or of the family of processes (Risken, 1996).Most commonly known is the Fokker-Planck equation or truncated forward Kolmogorov equation, partial differential equations, obtained from the Taylor expansion of the master equation.