By Mickaël D. Chekroun,Honghu Liu,Shouhong Wang

this primary quantity is anxious with the analytic derivation of particular formulation for the leading-order Taylor approximations of (local) stochastic invariant manifolds linked to a huge type of nonlinear stochastic partial differential equations. those approximations  take the shape of Lyapunov-Perron integrals, that are extra characterised in quantity II as pullback limits linked to a few partly coupled backward-forward platforms. This pullback characterization offers an invaluable interpretation of the corresponding approximating manifolds and results in an easy framework that unifies another approximation ways within the literature. A self-contained survey is additionally incorporated at the lifestyles and allure of one-parameter households of stochastic invariant manifolds, from the perspective of the idea of random dynamical systems.

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