Estimation of Kramers-Moyal coefficients at low sampling rates

Abstract

A new 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 approach that allows to calculate exact finite sampling interval effects by solving the adjoint Fokker-Planck equation. Therefore it is well suited for the analysis of sparsely sampled time series. The optimization can be performed either making a parametric ansatz for drift and diffusion functions or also parameter free. We demonstrate the power of the method in several numerical examples with synthetic time series.

6 pages, 5 figures

References in corpus (6)

• Finite sampling interval effects in Kramers-Moyal analysis
• Maximum Likelihood Estimation of Drift and Diffusion Functions
• Analysis of stochastic time series in the presence of strong measurement noise
• Markov properties in presence of measurement noise
• Exact corrections for finite-time drift and diffusion coefficients
• On low-sampling-rate Kramers-Moyal coefficients

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