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Zbl 0723.60074
Caraballo, Tomás
Asymptotic exponential stability of stochastic partial differential equations with delay. (English)
[J] Stochastics Stochastics Rep. 33, No.1-2, 27-47 (1990). ISSN 1045-1129; ISSN 1029-0346/e

The authors establish asymptotic stability for a linear stochastic partial differential equation with a delayed stochastic term of the form U(t-h)dW(t), where W(t) is a Wiener process on a separable Hilbert space, u(t) is the stochastic process and h is the delay time. This is a generalization of results in [{\it U. G. Haussmann}, J. Math. Anal. Appl. 65, 219-235 (1978; Zbl 0385.93051)] and [{\it A. Ichikawa}, SIAM J. Control Optimization 17, 152-174 (1979; Zbl 0434.93069)] and at the same time provides an alternative proof for these results.
[R.Curtain (Groningen)]

MSC 2000:: *60H15 Stochastic partial differential equations
93E15 Stochastic stability

Keywords: stochastic partial differential equations; pathwise asymptotic exponential stability; asymptotic stability

Citations: Zbl 0385.93051; Zbl 0434.93069

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Zentralblatt MATH Berlin [Germany]