Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations, 2015 Stochastic Manifolds for Nonlinear SPDEs II SpringerBriefs in Mathematics Series
Langue : Anglais
Auteurs : Chekroun Mickaël D., Liu Honghu, Wang Shouhong
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.
General Introduction.- Preliminaries.- Invariant Manifolds.- Pullback Characterization of Approximating, and Parameterizing Manifolds.- Non-Markovian Stochastic Reduced Equations.- On-Markovian Stochastic Reduced Equations on the Fly.- Proof of Lemma 5.1.-References.- Index.
Includes supplementary material: sn.pub/extras
Date de parution : 01-2015
Ouvrage de 129 p.
15.5x23.5 cm
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