Stochastic Optimal Prediction with Application to Averaged Euler Equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2000
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| _version_ | 1866908599913021440 |
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| author | Bell, John Chorin, Alexandre J. Crutchfield, William |
| author_facet | Bell, John Chorin, Alexandre J. Crutchfield, William |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_math_0008150 |
| institution | arXiv |
| publishDate | 2000 |
| record_format | arxiv |
| spellingShingle | Stochastic Optimal Prediction with Application to Averaged Euler Equations Bell, John Chorin, Alexandre J. Crutchfield, William Numerical Analysis 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. |
| title | Stochastic Optimal Prediction with Application to Averaged Euler Equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/math/0008150 |