ISSN:
1432-2064
Keywords:
60H15
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary A class of stochastic evolution equations with additive noise and weakly continuous drift is considered. First, regularity properties of the corresponding Ornstein-Uhlenbeck transition semigroupR t are obtained. We show thatR t is a compactC 0-semigroup in all Sobolev spacesW n,p which are built on its invariant measure μ. Then we show the existence, uniqueness, compactness and smoothing properties of the transition semigroup for semilinear equations inL p(μ) spaces and spacesW 1,p . As a consequence we prove the uniquencess of martingale solutions to the stochastic equation and the existence of a unique invariant measure equivalent to μ. It is shown also that the density of this measure with respect to μ is inL p(μ) for allp≧1.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01192465
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