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| Invariant Measures and Asymptotic Gaussian Bounds for Normal Forms of Stochastic Climate Model |
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Citation： |
Yuan YUAN,Andrew J. MAJDA.Invariant Measures and Asymptotic Gaussian Bounds for Normal Forms of Stochastic Climate Model[J].Chinese Annals of Mathematics B,2011,32(3):343~368 |
| Page view： 1790
Net amount： 1085 |
Authors： |
Yuan YUAN; Andrew J. MAJDA; |
Foundation： |
the National Science Foundation Grant (No. DMS-0456713) and the Office of
Naval Research Grant (No. N0014-05-1-1064). |
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| Abstract： |
The systematic development of reduced low-dimensional stochastic climate
models from observations or comprehensive high dimensional climate models is an important
topic for atmospheric low-frequency variability, climate sensitivity, and improved
extended range forecasting. Recently, techniques from applied mathematics have been
utilized to systematically derive normal forms for reduced stochastic climate models for
low-frequency variables. It was shown that dyad and multiplicative triad interactions combine
with the climatological linear operator interactions to produce a normal form with
both strong nonlinear cubic dissipation and Correlated Additive and Multiplicative (CAM)
stochastic noise. The probability distribution functions (PDFs) of low frequency climate
variables exhibit small but significant departure from Gaussianity but have asymptotic tails
which decay at most like a Gaussian. Here, rigorous upper bounds with Gaussian decay
are proved for the invariant measure of general normal form stochastic models. Asymptotic
Gaussian lower bounds are also established under suitable hypotheses. |
Keywords： |
Reduced stochastic climate model, Invariant measure, Fokker-Planck
equation, Comparison principle, Global estimates of probability density
function |
Classification： |
60H10, 60H30, 60E99, 35Q84 |
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