Beniamin Goldys, Bohdan Maslowski (2001)
Czechoslovak Mathematical Journal
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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 with .
Dorogovtsev, Andrey A. (2003)
International Journal of Mathematics and Mathematical Sciences
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Svetlana Janković (1998)
Zbornik Radova
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Ahmed, N.U., Ding, Xinhong (1993)
Journal of Applied Mathematics and Stochastic Analysis
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Fournier, Nicolas (2006)
Electronic Communications in Probability [electronic only]
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Bohdan Maslowski, Jan Seidler (1998)
Archivum Mathematicum
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The paper presents a review of some recent results on uniqueness of invariant measures for stochastic differential equations in infinite-dimensional state spaces, with particular attention paid to stochastic partial differential equations. Related results on asymptotic behaviour of solutions like ergodic theorems and convergence of probability laws of solutions in strong and weak topologies are also reviewed.