A viability theorem of stochastic semilinear evolution equations

A viability theorem of stochastic semilinear evolution equations is discussed under a dissipative condition in terms of uniqueness functions and a stochastic subtangential condition. Our strategy is to interpret a stochastic viability problem into a characterization problem of evolution operators associated with stochastic semilinear evolution equations. The main theorem is a generalization of the results due to Aubin and Da Prato in the case of stochastic differential equations in ℝ ^d .