Compactness in Lebesgue–Bochner spaces of random variables and the existence of mean-square random attractors
Keyword(s):
Let [Formula: see text] be a probability space and let [Formula: see text] be a separable Banach space. It is shown a subset [Formula: see text] of [Formula: see text], where [Formula: see text], is relatively compact in [Formula: see text] if and only if it is uniformly [Formula: see text]-integrable and uniformly tight. The additional condition of scalarly relatively compact required in the literature is shown to hold by a probabilistic argument. The result is then used to establish the existence of a mean-square random attractor for dissipative stochastic differential equations and stochastic parabolic partial differential equations.
2016 ◽
Vol 19
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pp. 173-186
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2014 ◽
Vol 66
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pp. 261-271
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1973 ◽
Vol 52
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pp. 189-211
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2010 ◽
Vol 15
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pp. 481-489
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2014 ◽
Vol 36
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pp. C1-C24
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