RECONSTRUCTION OF THE DETERMINISTIC DYNAMICS OF STOCHASTIC SYSTEMS

Abstract

We show that based on the mathematics of Markov processes and particularly based on the definition of Kramers–Moyal coefficients, it is possible to estimate the deterministic part of the dynamics for a broad class of nonlinear noisy systems. In particular, we show that for different kinds of noise perturbations, including non-Langevin force with finite correlation time and independent measurement noise, the deterministic part can be reconstructed.