Displaying similar documents to “Exponential stability of linear stochastic differential equations with bounded delay and the W-transform.”

The long-time behaviour of the solutions to semilinear stochastic partial differential equations on the whole space

Ralf Manthey (2001)

Mathematica Bohemica

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The Cauchy problem for a stochastic partial differential equation with a spatial correlated Gaussian noise is considered. The "drift" is continuous, one-sided linearily bounded and of at most polynomial growth while the "diffusion" is globally Lipschitz continuous. In the paper statements on existence and uniqueness of solutions, their pathwise spatial growth and on their ultimate boundedness as well as on asymptotical exponential stability in mean square in a certain Hilbert space of...