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A general method is proposed which allows one to estimate drift and diffusion coefficients of a stochastic process governed by a Langevin equation. It extends a previously devised approach [R. Friedrich et al., Physics Letters A 271, 217 (2000)], which requires sufficiently high sampling rates. The analysis is based on an iterative procedure minimizing the Kullback-Leibler distance between measured and estimated two time joint probability distributions of the process.
The generalized Langevin equation (GLE) overcomes the limiting Markov approximation of the Langevin equation by an incorporated memory kernel and can be used to model various stochastic processes in many fields of science ranging from climate modelin
Anomalous diffusion, process in which the mean-squared displacement of system states is a non-linear function of time, is usually identified in real stochastic processes by comparing experimental and theoretical displacements at relatively small time
Langevin models are frequently used to model various stochastic processes in different fields of natural and social sciences. They are adapted to measured data by estimation techniques such as maximum likelihood estimation, Markov chain Monte Carlo m
We propose an interpolation expression using the difference moment (Kolmogorov transient structural function) of the second order as the average characteristic of displacements for identifying the anomalous diffusion in complex processes when the sto
For reaction-diffusion processes with at most bimolecular reactants, we derive well-behaved, numerically tractable, exact Langevin equations that govern a stochastic variable related to the response field in field theory. Using duality relations, we