[[{"fid":"285","view_mode":"default","type":"media","field_deltas":{"1":{}},"fields":{},"attributes":{"height":"232","width":"153","style":"float: right;","class":"media-element file-default","data-delta":"1"}}]]This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems.

[[{"fid":"1718","view_mode":"default","fields":{"format":"default"},"type":"media","field_deltas":{"2":{"format":"default"}},"attributes":{"class":"media-element file-default","data-delta":"2"}}]]

%I Springer Briefs in Mathematics, Springer %C New York %P pp. 127 %G eng %U http://www.springer.com/us/book/9783319124957