Stochastic Optimal Prediction with Application to Averaged Euler Equations

Details Stochastic Optimal Prediction with Application to Averaged Euler Equations Stochastic Optimal Prediction with Application to Averaged Euler Equations

2000-08-18

arxiv.org/abs/math/0008150v1

Mathematics

Numerical Analysis

13 pages, 2 figures

Scientific paper

Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is approximated by its conditional expectation with respect to the invariant measure. In higher-order OP, unresolved information is approximated by a stochastic estimator, leading to a system of random or stochastic differential equations. We explain the ideas through a simple example, and then apply them to the solution of Averaged Euler equations in two space dimensions.

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