Center manifolds for stochastic evolution equations
Xiaopeng Chen, A. J. Roberts, Jinqiao Duan
TL;DR
This paper proves the existence and smoothness of center manifolds for stochastic evolution equations with multiplicative noise, under exponential trichotomy, and discusses their attraction and approximation properties.
Contribution
It establishes the existence and smoothness of stochastic center manifolds for a class of equations with multiplicative noise, expanding the theoretical understanding of stochastic dynamical systems.
Findings
Existence of stochastic center manifolds proved
Smoothness of these manifolds established
Discussion on exponential attraction and approximation included
Abstract
Stochastic invariant manifolds are crucial in modelling the dynamical behavior of dynamical systems under uncertainty. Under the assumption of exponential trichotomy, existence and smoothness of center manifolds for a class of stochastic evolution equations with linearly multiplicative noise are proved. The exponential attraction and approximation to center manifolds are also discussed.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Stochastic processes and financial applications · Mathematical Biology Tumor Growth