Two-parameter semigroups, evolutions and their applications to Markov and diffusion fields on the plane.
Mishura, Yu., Tomilov, Yu. (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Mishura, Yu., Tomilov, Yu. (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Zdzisław Brzeźniak, Szymon Peszat (1999)
Studia Mathematica
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Stochastic partial differential equations on are considered. The noise is supposed to be a spatially homogeneous Wiener process. Using the theory of stochastic integration in Banach spaces we show the existence of a Markovian solution in a certain weighted -space. Then we obtain the existence of a space continuous solution by means of the Da Prato, Kwapień and Zabczyk factorization identity for stochastic convolutions.
Bohdan Maslowski (1995)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Patrick Cattiaux, Christian Léonard (1996)
Séminaire de probabilités de Strasbourg
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Svetlana Janković (1998)
Zbornik Radova
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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 .
Ahmed, N.U. (1991)
Journal of Applied Mathematics and Stochastic Analysis
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B. Maslowski, I. Simão (1997)
Colloquium Mathematicae
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