Geodesic
Inertial manifolds and stationary measures for stochastically perturbed dissipative dynamical systems
Sbornik. Mathematics, Tome 186 (1995) no. 1, pp. 29-45

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We prove the existence of inertial manifolds for a semilinear dynamical system perturbed by additive ‘white noise’. This manifold is generated by a certain predictable stationary vector process $\Phi_t(\omega)$. We study properties of this process as well as the properties of the induced finite-dimensional stochastic system on the manifold (inertial form). The results obtained allow us to prove for the original stochastic system a theorem on stabilization of stationary solutions to a unique invariant measure. This measure is uniquely defined by the probability distribution of the process $\Phi_t(\omega)$ and the form of the invariant measure corresponding to the inertial form. 
@article{SM_1995_186_1_a1,
     author = {T. V. Girya and I. D. Chueshov},
     title = {Inertial manifolds and stationary measures for stochastically perturbed dissipative dynamical systems},
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     volume = {186},
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     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_1_a1/}
}
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T. V. Girya; I. D. Chueshov. Inertial manifolds and stationary measures for stochastically perturbed dissipative dynamical systems. Sbornik. Mathematics, Tome 186 (1995) no. 1, pp. 29-45. http://geodesic.mathdoc.fr/item/SM_1995_186_1_a1/