Absolute stability of a stochastic evolution equationt

It is shown that mean square stability of a class of nonlinear stochastic evolution equations is equivalent to that of a linear stochastic evolution equation provided noise terms in the former are dominated by that of the latter. This generalizes Morozan's result concerning the stochastic dserential equation of Lur'e type to a much wider class of stochastic evolution equations in Hilbert space. Two examples are given to illustrate the theory.