Non-Markovian Optimal Prediction

Preprint

3 January 2001

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0101022

Abstract

Optimal prediction methods compensate for a lack of resolution in the numerical solution of complex problems through the use of prior statistical information. We know from previous work that in the presence of strong underresolution a good approximation needs a non-Markovian "memory", determined by an equation for the "orthogonal", i.e., unresolved, dynamics. We present a simple approximation of the orthogonal dynamics, which involves an ansatz and a Monte-Carlo evaluation of autocorrelations. The analysis provides a new understanding of the fluctuation-dissipation formulas of statistical physics. An example is given.

Keywords

PREDICTION METHODS
OPTIMAL PREDICTION
NUMERICAL SOLUTION
MARKOVIAN OPTIMAL
UNDERRESOLUTION
APPROXIMATION
STATISTICAL
MONTE CARLO

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Version 1, 2001-01-03, ArXiv

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