Measure theory and S^{2}-pseudo almost periodic and automorphic process: application to stochastic evolution equations

摘要: In this work, we use the measure theory to define and study spaces of Stepanov-like $$\mu $$ -pseudo almost ( $$S^{2}$$ - almost) periodic automorphic processes in square mean sense. We establish many interesting results on functional such like completeness composition theorems. The main objective paper is existence, uniqueness stability square-mean (resp. automorphic) mild solution a linear semilinear case stochastic evolution equations when functions forcing are both continuous verify some suitable assumptions. technique analysis used achieve required theory, theorems Banach fixed point theorem. provide an example illustrate ours results.