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DY: Dynamik und Statistische Physik

DY 31: Nonlinear Stochastic Systems I

DY 31.2: Vortrag

Montag, 7. März 2005, 10:45–11:00, TU H2032

Estimation of Drift and Diffusion Functions of Stochastic Processes — •David Kleinhans and Rudolf Friedrich — Institut für Theoretische Physik, Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster

We present a general method to extract drift and diffusion functions from experimental time series. This is based on a procedure recently published by Siegert et al[1]. However, our approach does not perform any limiting procedure regarding the sampling rate.

Drift and diffusion coefficients are embledded into families of functions depending on a set of parameters σ. A first estimate is given by the evaluation of drift and diffusion using the smallest availible time increment[1]. An optimal set of parameters is obtained by an iteration procedure minimizing the Kullback-Leibler distance between the measured and the calculated two point joined pdf. This pdf is obtained either by a simulation of the langevin equation of a numerical solution of the corresponding Fokker-Planck equation for the parameter set σ.

For unidimensional data our method substantially can be simplified to analyse processes containing additive and multiplicative noise terms.

[1] S. Siegert et al., Physics Letters A 234, 275-280 (1998)