Improved estimation of Fokker-Planck equations through optimisation

Abstract

An improved method for the description of hierarchical complex systems by means of a Fokker-Planck equation is presented. In particular the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm for constraint problems (L-BFGS-B) is used to minimize the distance between the numerical solutions of the Fokker-Planck equation and the empirical probability density functions and thus to estimate properly the drift and diffusion term of the Fokker-Planck equation. The optimisation routine is applied to a time series of velocity measurements obtained from a turbulent helium gas jet in order to demonstrate the benefits and to quantify the improvements of this new optimisation routine.

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• Extracting strong measurement noise from stochastic series: applications to empirical data
• Analysis of stochastic time series in the presence of strong measurement noise
• Instantons and the path to intermittency in turbulent flows
• Master equation for She-Leveque scaling and its classification in terms of other Markov models of developed turbulence
• Non-parametric estimation of a Langevin model driven by correlated noise
• Markov property of Lagrangian turbulence