| Título: | Invariant measures for stochastic Cauchy problems with asymptotically unstable drift semigroup |
| Autores: |
Gaans, Onno van; Leiden University Neerven, Jan van; Technical University of Delft |
| Fecha: | 2006-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Invariant measures, stochastic evolution equations in Hilbert spaces 35R15, 47D06, 60H05 |
| Descripción: | 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. |
| Idioma: | No aplica |
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