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Invariant measures for stochastic Cauchy problems with asymptotically unstable drift semigroup


 
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1. Title Title of document Invariant measures for stochastic Cauchy problems with asymptotically unstable drift semigroup
 
2. Creator Author's name, affiliation, country Onno van Gaans; Leiden University
 
2. Creator Author's name, affiliation, country Jan van Neerven; Technical University of Delft
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Invariant measures, stochastic evolution equations in Hilbert spaces
 
3. Subject Subject classification 35R15, 47D06, 60H05
 
4. Description Abstract We investigate existence and permanence properties of invariant measures for abstract stochastic Cauchy problems of the form $$dU(t) = (AU(t)+f)\,dt + B\,dW_H(t), \ \ t\ge 0,$$ governed by the generator $A$ of an asymptotically unstable $C_0$-semigroup on a Banach space $E$. Here $f \in E$ is fixed, $W_H$ is a cylindrical Brownian motion over a separable real Hilbert space $H$, and $B$ is a bounded operator from $H$ to $E$. We show that if $E$ does not contain a copy of $c_0$, such invariant measures fail to exist generically but may exist for a dense set of operators $B$. It turns out that many results on invariant measures which hold under the assumption of uniform exponential stability of $S$ break down without this assumption.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Research Training Network HPRN-CT-2002-00281 (authors 1 and 2); NWO VIDI subsidie 639.032.201 (author 2)
 
7. Date (YYYY-MM-DD) 2006-03-29
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1184
 
10. Identifier Digital Object Identifier 10.1214/ECP.v11-1184
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 11
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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