Bounded solutions of affine stochastic differential equations and stability.(English)Zbl 0606.60056

For affine Ito equations with bounded coefficients it is proved that the existence of a solution with bounded expectation and covariance implies the exponential stability in mean square of the corresponding linear stochastic equation.
The existence of a trajectory of a flow defined on the space of probability laws corresponding to solutions bounded on the whole axis is proved under the exponential stability of the linear system associated with the affine Ito equation.

MSC:

 60H20 Stochastic integral equations 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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