Stochastic Parameterizing Manifolds and Non Markovian Reduced Equations is popular PDF and ePub book, written by Mickaël D. Chekroun in 2014-12-23, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Stochastic Parameterizing Manifolds and Non Markovian Reduced Equations can be Read Online from any device for your convenience.
Stochastic Parameterizing Manifolds and Non Markovian Reduced Equations Book PDF Summary
In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.
Detail Book of Stochastic Parameterizing Manifolds and Non Markovian Reduced Equations PDF
- Author : Mickaël D. Chekroun
- Release : 23 December 2014
- Publisher : Springer
- ISBN : 9783319125206
- Genre : Mathematics
- Total Page : 141 pages
- Language : English
- PDF File Size : 10,9 Mb
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