Abstract
The paper deals with systems of ODEs containing polynomial nonlinearities and random inhomogeneous terms. Applying perturbation method pathwise solutions are found in form of power series with respect to a parameter η controlling the nonlinearities. Under the assumption that for η=0 the system is stable and that the inhomogeneous terms are bounded the radius of convergence of the perturbation series is estimated. Further, it is proved that the perturbation series form stationary solutions if the inhomogeneous terms are stationary.
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