Geodesic
Uniform exponential ergodicity of stochastic dissipative systems
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 4, pp. 745-762

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We study ergodic properties of stochastic dissipative systems with additive noise. We show that the system is uniformly exponentially ergodic provided the growth of nonlinearity at infinity is faster than linear. The abstract result is applied to the stochastic reaction diffusion equation in $\mathbb{R}^d$ with $d\le 3$.
Classification : 37A30, 47A35, 60H10, 60H15, 60J99
Keywords: dissipative system; compact semigroup; exponential ergodicity; spectral gap 
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     author = {Goldys, Beniamin and Maslowski, Bohdan},
     title = {Uniform exponential ergodicity of stochastic dissipative systems},
     journal = {Czechoslovak Mathematical Journal},
     pages = {745--762},
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     volume = {51},
     number = {4},
     year = {2001},
     mrnumber = {1864040},
     zbl = {1001.60067},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2001__51_4_a6/}
}
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Goldys, Beniamin; Maslowski, Bohdan. Uniform exponential ergodicity of stochastic dissipative systems. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 4, pp. 745-762. http://geodesic.mathdoc.fr/item/CMJ_2001__51_4_a6/