Smoothness of invariant manifolds for stochastic evolution equations with non-dense domain

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With the crucial estimation of random Stieltjes-type convolution, the Lyapunov–Perron method allows us to establish the existence of invariant dynamics for stochastic evolution equation with non-dense domain. In this paper, we develop the conditions for [Formula: see text]-smoothness of center manifold for such equation with linear multiplicative noise, unstable manifold and stable set for the one with nonlinear multiplicative noise as well. Our result may apply to a broad range of stochastic systems with non-dense domain beyond Brownian noise.