TY - JOUR
T1 - Non-Markovian optimal prediction
AU - Chorin, Alexandre J.
AU - Hald, Ole H.
AU - Kupferman, Raz
PY - 2001/1
Y1 - 2001/1
N2 - Optimal prediction methods compensate for a lack of resolution in the numerical so lution 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.
AB - Optimal prediction methods compensate for a lack of resolution in the numerical so lution 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.
UR - http://www.scopus.com/inward/record.url?scp=0002051595&partnerID=8YFLogxK
U2 - 10.1515/mcma.2001.7.1-2.99
DO - 10.1515/mcma.2001.7.1-2.99
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AN - SCOPUS:0002051595
SN - 0929-9629
VL - 7
SP - 99
EP - 109
JO - Monte Carlo Methods and Applications
JF - Monte Carlo Methods and Applications
IS - 1-2
ER -