Schütte, Ch. and Walter, J. and Hartmann, C. and Huisinga, W. (2004) An Averaging Principle for Fast Degrees of Freedom Exhibiting LongTerm Correlations. Multiscale Model. Simul., 2 (3). pp. 501526.

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Official URL: http://dx.doi.org/10.1137/030600308
Abstract
This article is concerned with the averaging principle and its extensions for stochastic dynamical systems with fast and slow degrees of freedom. It is demonstrated how the "conventional" averaging principle results from asymptotic multiscale analysis, how one can construct an indicator for its (in)appropriateness, and how, if inappropriate, it may be extended into an improved approximation. The conventional scheme contains averages over the entire accessible state space of the fast degrees of freedom and may thus fail if these fast degrees of freedom exhibit longterm (auto)correlations. In contrast, the improved scheme combines several conditional averages with a Markov jump process that is designed to represent the flipping process between the conditional averages and thus incorporates the important longterm correlations. All important steps of the derivation are illustrated by numerical experiments. Application to problems from molecular dynamics is discussed.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics Department of Mathematics and Computer Science > Institute of Mathematics > Cellular Mechanics Group Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group 
ID Code:  62 
Deposited By:  Admin Administrator 
Deposited On:  03 Jan 2009 20:20 
Last Modified:  03 Mar 2017 14:39 
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