Stochastic modelling: replacing fast degrees of freedom by noise

Just, W.; Kantz, H.; Rödenbeck, C.; Helm, M.

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Stochastic modelling: replacing fast degrees of freedom by noise

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Rödenbeck, C.
Inverse Data-driven Estimation, Dr. C. Rödenbeck, Department Biogeochemical Systems, Prof. M. Heimann, Max Planck Institute for Biogeochemistry, Max Planck Society;

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Just, W., Kantz, H., Rödenbeck, C., & Helm, M. (2001). Stochastic modelling: replacing fast degrees of freedom by noise. Journal of Physics A: Mathematical and General, 34(15), 3199-3213.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000E-CDDC-1

Abstract

In systems with timescale separation, where the fast degrees of freedom exhibit chaotic motion, the latter are replaced by suitable stochastic processes. A projection technique is employed to derive equations of motion for the phase space density of the slow variables by eliminating the fast ones. The resulting equations can be approximated in a controlled way by Fokker-Planck equations or equivalently by stochastic differential equations for slow degrees of freedom. We discuss some model situations and explore the accuracy of the approximations by numerical simulations. [References: 16]