How to cite item

Invariant measures for stochastic Cauchy problems with asymptotically unstable drift semigroup

   
@article{ECP1184,
	author = {Onno Gaans and Jan Neerven},
	title = {Invariant measures for stochastic Cauchy problems with asymptotically unstable drift semigroup},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {11},
	year = {2006},
	keywords = {Invariant measures, stochastic evolution equations in Hilbert spaces},
	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.},
	pages = {no. 3, 24-34},
	issn = {1083-589X},
	doi = {10.1214/ECP.v11-1184},    
        url = {http://ecp.ejpecp.org/article/view/1184}}