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Asymptotic exponential stability of stochastic partial differential equations with delay. (English) Zbl 0723.60074
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 [U. G. Haussmann, J. Math. Anal. Appl. 65, 219-235 (1978; Zbl 0385.93051)] and [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.
MSC:
60H15Stochastic partial differential equations
93E15Stochastic stability