Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1033.60074
El-Borai, Mahmoud M.; Moustafa, Osama L.; Ahmed, Hamdy M.
Asymptotic stability of some stochastic evolution equations.
(English)
[J] Appl. Math. Comput. 144, No. 2-3, 273-286 (2003). ISSN 0096-3003

The authors study the Hilbert space-valued stochastic differential equation $$dX+(A+Q)Xdt=BX dW,$$ where A is the generator of a strongly continuous semigroup $U(t)$, $W$ is a Hilbert space-valued Brownian motion, $B$ is a bounded linear operator and $Q$ is a general closed linear operator. Under the hypothesis of exponential stability of the semigroup $U(t)$ and a growth condition on $Q$ there exists a mild solution to this equation that has certain stability properties: for $t\to\infty$ the solution converges exponentially fast to zero in a mean square as well as in a pathwise sense.
[Markus Reiss (Berlin)]
MSC 2000:
*60H15 Stochastic partial differential equations

Keywords: stochastic evolution equations; exponential stability; mild solution

Highlights
Master Server