Square-mean pseudo almost automorphic process and its application to stochastic evolution equations (Q537712)

The authors originate a stochastic version of the theory of almost almost automorphy. At first, definitions of abstract spaces and square-mean pseudo almost automorphic processes are introduced. Some results not only on the completeness of the space of square-mean pseudo almost automorphic processes but also on the composition of such processes are included. Then, based on these results, existence as well as uniqueness of square-mean pseudo almost automorphic solutions to linear stochastic evolution equations are proved. Several theorems are established concerning the global stability of square-mean pseudo almost automorphic solutions to linear SEEs. Finally, an example is provided to show the feasibility of the developed theoretical results.